Answer:
a) The sampling distributio will be normal with mean 600 and standard deviation 11.07.
b) - 68% of the samples will have means between 589 and 611 apples per tree.
- 95% of the samples will have means between 578 and 622 apples per tree.
- 99.7% of the samples will have means between 567 and 633 apples per tree.
c) The probability that a random sample of 40 trees has an average amount of apples of 620 pounds or higher is 0.035.
Step-by-step explanation:
a) The sampling distribution for a population with mean of 600 pounds and standard deviation of 70 pounds, with a sample size of 40 trees, will have the following parameters:
[tex]\mu_s=\mu=600\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{70}{\sqrt{40}}=\dfrac{70}{6.325}=11.07[/tex]
b) Using the 68-95-99.7 rule for the sampling distribution, we can tell that:
- 68% of the samples will have means between 589 and 611 apples per tree.
[tex]X_1=\mu+z_1\cdot\sigma/\sqrt{n}=600-1\cdot 70\sqrt{40}=600-11=589\\\\X_2=\mu+z_2\cdot\sigma/\sqrt{n}=600+1\cdot 70\sqrt{40}=600+11=611[/tex]
- 95% of the samples will have means between 578 and 622 apples per tree.
[tex]X_1=\mu+z_1\cdot\sigma/\sqrt{n}=600-2\cdot 70\sqrt{40}=600-22=578\\\\X_2=\mu+z_2\cdot\sigma/\sqrt{n}=600+2\cdot 70\sqrt{40}=600+22=622[/tex]
- 99.7% of the samples will have means between 567 and 633 apples per tree.
[tex]X_1=\mu+z_1\cdot\sigma/\sqrt{n}=600-3\cdot 70\sqrt{40}=600-33=567\\\\X_2=\mu+z_2\cdot\sigma/\sqrt{n}=600+3\cdot 70\sqrt{40}=600+33=633[/tex]
c) We can calculate the probability with the z-score for X=620.
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{620-600}{70/\sqrt{40}}=\dfrac{20}{11.068}=1.807\\\\\\P(X>620)=P(z>1.807)=0.035[/tex]
The probability that a random sample of 40 trees has an average amount of apples of 620 pounds or higher is 0.035.
To every linear transformation T from R2 to R2, there is an associated 2×2 matrix. Match the following linear transformations with their associated matrix.
1. Clockwise rotation by π/2 radians
2. Reflection about the x-axis
3. Counterclockwise rotation by π/2 radians
4. The projection onto the x-axis given by T(x,y) = (x,0)
5. Reflection about the y-axis e
6. Reflection about the line y = x
A. (-1 0, 0 1)
B. (0 1, 1 0)
C. (1 0, 0 0)
D. (0 1, -1 0)
E. (1 0, 0 -1)
F. (0 -1, 1 0)
G. None of the above
Answer:
1. Clockwise rotation by π/2 radians
: D
2. Reflection about the x-axis
: E
3. Counterclockwise rotation by π/2 radians
: F
4. The projection onto the x-axis given by T(x,y) = (x,0)
: C
5. Reflection about the y-axis : A
6. Reflection about the line y = x : B
Step-by-step explanation:
Given a linear transformation [tex]T:\mathbb{R}^2\to\mathbb{R}^2[/tex], one matrix representation of T is obtained by stacking the vectors T(1,0) and T(0,1) in columns.
a) A counter clockwise rotation of [tex]\pi/2[/tex] radians sends (1,0) to (0,-1) and it sends (0,1) to (1,0), so the matrix representation is
[tex]\left[\begin{matrix} 0& 1 \\ -1 & 0 \end{matrix}\right][/tex] which corresponds to matrix D.
From now on, I will provide the values of T(1,0) and T(0,1)
b) Reflection about the x-axis T(1,0) = (1,0) and T(0,1) = (0,-1), which corresponds to matrix E.
c) Counterclockwise rotation by π/2 radians T(1,0) = (0,1), T(0,1) = (-1,0). Matrix F
d) The projection onto the x-axis given by T(x,y) = (x,0). T(1,0) = (1,0) T(0,1) = (0,0). Matrix C
e) Reflection about the y-axis T(1,0) = (-1,0) T(0,1) = (0,1). Matrix A
f) Reflection about the line y = x. This transformation corresponds to interchanging the values of x and y. That is, send (x,y) to (y,x). So, in this case
T(1,0) = (0,1) T(0,1) = (1,0). Matrix B
Male players at the high school, college, and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.2 ounces. Assume that the weights of basketballs are approximately normally distributed. If a basketball is randomly selected, what is the probability that it will weigh between 21.4 and 23.8 ounces
Answer:
The probability that a basketball will weigh between 21.4 and 23.8 ounces is 0.62465.
Step-by-step explanation:
We have all this information from the question:
The weights of the basketballs are approximately normally distributed.The population mean, [tex] \\ \mu[/tex], for basketball weights is 22.0 ounces, [tex] \\ \mu = 22[/tex] ounces.The population standard deviation, [tex] \\ \sigma[/tex], for basketball weights is 1.2 ounces, [tex] \\ \sigma = 1.2[/tex] ounces.To answer this question:
First, we need to calculate the cumulative probability for [tex] \\ x = 21.4[/tex] ounces and [tex] \\x = 23.8[/tex] ounces. Second, subtract both values to obtain the asked probability, that is the probability that [a basketball] will weigh between 21.4 and 23.8 ounces.Important concepts to remember:
For this, it is crucial three concepts: the standard normal distribution, the standard normal table, and z-scores:
Roughly speaking, the standard normal distribution is a normal distribution for standardized values. We can obtain standardized values using the formula for z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
And these values represent the distance from the population mean in standard deviation units. When they are positive, these values are above the population mean, [tex] \\ \mu[/tex]. In case they are negative, they are below [tex] \\ \mu[/tex].
We can obtain probabilities for any normally distributed data using the standard normal distribution. These values are tabulated into the standard normal table, available in Statistics books or on the Internet.
In general, these values are cumulative probabilities, that is, probabilities from [tex] \\ -\infty[/tex] to the value x in question (a raw value).
At this stage, we have enough information to solve the question.
Solving the question
Cumulative probability for [tex] \\ P(X<21.4)[/tex] ounces.
Obtain the z-score, using [1], for [tex] \\ x = 21.4[/tex] ounces (without using units):[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{21.4 - 22}{1.2}[/tex]
[tex] \\ z = \frac{-0.6}{1.2}[/tex]
[tex] \\ z = -0.5[/tex]
That is, the raw score [tex] \\ x = 21.4[/tex] is 0.5 standard deviations below, [tex] \\ z = -0.5[/tex], the population mean.
Getting [tex] \\ P(X<21.4) = P(Z<-0.5)[/tex] using the standard normal table.Since [tex] \\ P(X<21.4) = P(Z<-0.5)[/tex], we can consult the standard normal table, using [tex] \\ z = -0.5[/tex] as an entry (using its first column).
The first row of this table has a second digit in the decimal part for the value of z. In this case, this second digit is zero (or to be more precise, -0.00), because [tex] \\ z = -0.50[/tex]. With the intersection of these two values in the table, namely, -0.5 and -0.00, we finally obtain the cumulative probability, [tex] \\ P(Z<-0.50) = 0.30854[/tex].
Thus, [tex] \\ P(X<21.4) = P(Z<-0.50) = 0.30854[/tex]
Cumulative probability for [tex] \\ P(X<23.8)[/tex] ounces.
We can follow the same steps as before:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{23.8 - 22.0}{1.2}[/tex]
[tex] \\ z = \frac{1.8}{1.2}[/tex]
[tex] \\ z = 1.5[/tex]
[tex] \\ P(X<23.8) = P(Z<1.5) = 0.93319[/tex] using the standard normal table (z =1.5, +0.00).
Therefore, [tex] \\ P(X<23.8) = P(Z<1.5) = 0.93319[/tex]
Then, to answer the probability that a basketball will weigh between 21.4 and 23.8 ounces, we subtract (as we mentioned before) both cumulative probabilities:
[tex] \\ P(21.4 < X < 23.8) = P(-0.5 < Z < 1.5) = P(X<23.8) - P(X<21.4) = P(Z<1.5) - P(Z<-0.5) = 0.93319 - 0.30854 = 0.62465[/tex]
Then, the probability that a basketball will weigh between 21.4 and 23.8 ounces is 0.62465.
We can see this probability represented by the shaded area in the below graph.
Mario has $150 to spend on food for a party. He ordered pizzas that cost $8 each and bottles of soda that cost $2 each which inequality represents how much he can
spend without running out of money?
Answer:
8p + 2s <= 150
Step-by-step explanation:
Let p = number of a pizza.
Let s = price of a bottle of soda.
The inequality is
8p + 2s <= 150
There are 48 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.)
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?
Answer:
a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.
b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n trials, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
In this question:
[tex]n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71[/tex]
These values are in minutes.
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{250 - 240}{27.71}[/tex]
[tex]Z = 0.36[/tex]
[tex]Z = 0.36[/tex] has a pvalue of 0.6406
64.06% probability that he is through grading before the 11:00 P.M. TV news begins.
(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?
The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.
Compute the standard error for sample proportions from a population with proportion p= 0.55 for sample sizes of n=30, n=100 and n=1000 . Round your answers to three decimal places.
Given Information:
Population proportion = p = 0.55
Sample size 1 = n₁ = 30
Sample size 2 = n₂ = 100
Sample size 3 = n₃ = 1000
Required Information:
Standard error = σ = ?
Answer:
[tex]$ \sigma_1 = 0.091 $[/tex]
[tex]$ \sigma_2 = 0.050 $[/tex]
[tex]$ \sigma_3 = 0.016 $[/tex]
Step-by-step explanation:
The standard error for sample proportions from a population is given by
[tex]$ \sigma = \sqrt{\frac{p(1-p)}{n} } $[/tex]
Where p is the population proportion and n is the sample size.
For sample size n₁ = 30
[tex]$ \sigma_1 = \sqrt{\frac{p(1-p)}{n_1} } $[/tex]
[tex]$ \sigma_1 = \sqrt{\frac{0.55(1-0.55)}{30} } $[/tex]
[tex]$ \sigma_1 = 0.091 $[/tex]
For sample size n₂ = 100
[tex]$ \sigma_2 = \sqrt{\frac{p(1-p)}{n_2} } $[/tex]
[tex]$ \sigma_2 = \sqrt{\frac{0.55(1-0.55)}{100} } $[/tex]
[tex]$ \sigma_2 = 0.050 $[/tex]
For sample size n₃ = 1000
[tex]$ \sigma_3 = \sqrt{\frac{p(1-p)}{n_3} } $[/tex]
[tex]$ \sigma_3 = \sqrt{\frac{0.55(1-0.55)}{1000} } $[/tex]
[tex]$ \sigma_3 = 0.016 $[/tex]
As you can notice, the standard error decreases as the sample size increases.
Therefore, the greater the sample size lesser will be the standard error.
Im need help on this question
A car is leaving New York. After 30 minutes, the car is 25 miles from New York, and after 3 hours the car is 200 miles from New York. What is the car's average speed (miles per hour) between the 30 minute and 3 hour time frame
Answer:
57.1428571429 miles per hour Round off the answer to what your teacher asked.
Step-by-step explanation:
Since we want final answer in miles per hour, lets change the 30 mins to 0.5 hours
Phase 1 =25miles per 0.5 hours
Phase 2 = (200miles-25miles) per 3 hours
Speed = distance/time
Average speed = total distance/ time
Total distance is 200miles because both phases say from new york that means it travels 25 miles away from new york then 3 hours later it is 200 miles away from new york
total time =3 hours+0.5 hours = 3.5 hours
Average speed = 200/3.5
Average speed = 57.1428571429 miles per hour
Rate brainliest please
We want to get the average speed between the 30 minute and 3-hour time frame.
The average speed in that time frame is 70 miles per hour.
We will define average speed as the quotient between the distance travelled and the time it takes to travel that distance.
We know that at 30 minutes, the car is 25 miles away from NY
At 3 hours, the car is 200 miles away from NY.
So the distance travelled in that time frame is:
200 miles - 25 miles = 175 miles.
And the time between 30 minutes and 3 hours is just:
3 h - 0.5h = 2.5 h
So the average speed is:
S = (175 mi)/(2.5 h) = 70 mi/h
The average speed is 70 miles per hour.
If you want to learn more, you can read:
https://brainly.com/question/9834403
which substitution should be used to rewrite 16(x^3+1)^2-22(x^3+1)-3=0 as a equation?
Answer:
The factorized form will be {(2x^3)-1}×{(8x^3)+9}=0
The simplified form will be (16x^6)+(10x^3)-9=0
Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative StartFraction 7 Over 4 EndFraction – 3x – 5 + 4x = –. A table titled Deepak's Solution with 3 columns and 5 rows. The first row is, blank, Steps, Resulting equation. The second row has the entries, 1, Use the distributive property to simplify. StartFraction 5 Over 2 minus 5 plus 4 x minus 3 x equals negative StartFraction 7 Over 4 EndFraction. The third row has the entries, 2, Simplify by combining like terms, negative StartFraction 5 Over 2 plus x equals negative StartFraction 7 Over 4 EndFraction. The fourth row has the entries, 3, Use the addition property of equality, negative StartFraction 5 Over 2 EndFraction plus StartFraction 5 Over 2 EndFraction plus x equals negative StartFraction 7 Over 4 EndFraction plus StartFraction 10 Over 4 EndFraction. The fifty row has the entries, 4, Simplify by combining like terms, x equals StartFraction 3 Over 4 EndFraction. Which step has an incorrect instruction? Step 1 Step 2 Step 3 Step 4
Answer:
Step 1
Step-by-step explanation:
Deepak given problem is: [tex]\dfrac52-3x-5+4x=-\dfrac74[/tex]
[tex]\left|\begin{array}{c|cc}$Steps&$Resulting Equation\\$1, Use the distributive property to simplify.&\dfrac52-5+4x-3x=-\dfrac74\\$2, Simplify by combining like terms&-\dfrac52+x=-\dfrac74\end{array}\right|[/tex]
[tex]\left|\begin{array}{c|cc}$3, Use the addition property of equality&-\dfrac52+\dfrac52+x=-\dfrac74+\dfrac{10}{4}\\$4, Simplify by combining like terms&x=\dfrac34\end{array}\right|[/tex]
In Step 1, he simply rearranged like terms. He did not use the distributive property. Therefore, the instruction in Step 1 was incorrect.
Answer:
step 1
Step-by-step explanation:
A least squares regression line: a. may be used to predict a value of y if the corresponding x value is given b. implies a cause-effect relationship between x and y c. can only be determined if a good linear relationship exists between x and y d. None of these alternatives is correct.
Answer:
a) May be used to predict a value of y if the corresponding x value is given
Step-by-step explanation:
In regression analysis, the vertical distance from the regression line to the data points can be minimized using the least square regression line.
Given the example of a least square regression equation:
y = ax + b
Where
a = slope
b = Y-intercept
If the value of x is known, the value of y may be predicted.
Option A is correct.
A least squares regression line may be used to predict a value of y if the corresponding x value is given
The least square regression line implies a mathematical equation which models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given.
The least square regression line also called the best fit line, gives a mathematical relationship between variables in slope - intercept form. The predicted value of y or x if the corresponding value of either variable is given.Hence, the most appropriate option is "
may be used to predict a value of y if the corresponding x value is given."
Learn more : https://brainly.com/question/16975425
PLEASE HELP!
A farmer wanted to paint a shed out in his field. Here is the breakdown of the dimensions: the building is sitting on a square slab of cement that is 10' x 10'. It is 8 feet from the bottom of the shed to the bottom of the roof on the edge, and 10 feet from the bottom of the shed to the top of the very tip top of the roof. So A = 10, B = 8 and C = 10. Using the formula for the area of a rectangle, A = l x w and the area of a triangle, 1/2(bh), b is base and h is height, then find the total area that needs to be painted. Total area =
Answer:
340 square feet
Step-by-step explanation:
If we "unwrap" the painted surface from the shed, it will have the shape shown in the attachment. It is essentially a 40' by 8' rectangle with two 10' wide by 2' high triangles added.
The rectangle area is ...
A = LW = (40 ft)(8 ft) = 320 ft²
The total area of the two triangles is ...
A = 2(1/2)bh = (10 ft)(2 ft) = 20 ft²
Then the painted area is ...
total area = 320 ft² +20 ft²
total area = 340 ft²
simplify 5m - m - m +3
Answer:
Brainliest!Step-by-step explanation:
5m-m-m+3
5m-2m+3
3m+3
Answer: 3m + 3
Explanation: If there's no coefficient in front of the variable, you can give it a coefficient of 1, so the -m can be thought of as -1m.
So our problem can be read as 5m - 1m - 1m + 3.
Now combine like terms.
Since 5m, -1m, and -1m are terms that contain an m, we can combine.
So 5m - 1m - 1m simplifies to 3m.
So our answer is 3m + 3
a painter paints the side of a house at a rate of 3 square feet per minute. if the dimensions of the side of the house are 15 feet by 18, how many minutes does it take the painter to finish the job?
Answer: 90 minutes
Step-by-step explanation:
Area of the side = 15 x 18 = 270 sq. ft.
3 sq. ft take a minute to paint
270 sq. ft. will take 270 / 3
= 90 minutes
A random sample of 16 apartments in NYC showed that the average rent is $2,850 with standard deviation of $50. Assume normal distribution. Test the claim that the average rent has increased at α= 0.05
Answer:
At α= 0.05, there is enough evidence to support the claim that the average rent has increased from $2800.
P-value = 0.001.
Step-by-step explanation:
The question is incomplete:
The average monthly rent for a one bedroom apartment in NYC was $2,800 in 2013. A random sample of 16 apartments in NYC showed that the average rent is $2,850 with standard deviation of $50. . Test the claim that the average rent has increased at α= 0.05.
This is a hypothesis test for the population mean.
The claim is that the average rent has increased from $2800.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=2800\\\\H_a:\mu> 2800[/tex]
The significance level is 0.05.
The sample has a size n=16.
The sample mean is M=2850.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=50.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{50}{\sqrt{16}}=12.5[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2850-2800}{12.5}=\dfrac{50}{12.5}=4[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=16-1=15[/tex]
This test is a right-tailed test, with 15 degrees of freedom and t=4, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>4)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average rent has increased from $2800.
George earned e extra credit points. Kate earned 35 fewer extra credit points than George. Choose the expression that
shbws how many extra credit points Kate earned.
O A. 35
B.35e
C.35 + e
D. e - 35
Ronat Selection
Answer:
D. e - 35
Step-by-step explanation:
We have that:
George earned e extra points.
Kate earned k extra points.
Kate earned 35 fewer extra credit points than George.
This means that k is e subtracted by 35, that is:
k = e - 35
So the correct answer is:
D. e - 35
An airplane is at 32,000 feet above sea level
Answer:
is that the question because I'm not sure
Answer:
whats the full question
Step-by-step explanation:
Calculate the interest produced by a principal of $ 4,500 at 5% annual simple interest in 8 months.
Answer:
4,500 x 5 = 22,500
4,500 divided by 5 = 900
4,500 plus 5 = 4,505
4,500 minus 5 = 4,495
Step-by-step explanation:
it is either one of those that u have to choose from good luck
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 255.4 and a standard deviation of 63.9. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 63.7 and 447.1? b. What is the approximate percentage of women with platelet counts between 191.5 and 319.3?
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data
b) [tex] P(191.5<X<319.5)[/tex]
We can find the number of deviations from the mean for the limits using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{191.5-255.4}{63.9}= -1[/tex]
[tex] z=\frac{319.3-255.4}{63.9}= 1[/tex]
So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case
Step-by-step explanation:
For this case we have the following properties for the random variable of interest "blood platelet counts"
[tex]\mu = 255.4[/tex] represent the mean
[tex]\sigma = 63.9[/tex] represent the population deviation
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data
Part b
We want this probability:
[tex] P(191.5<X<319.5)[/tex]
We can find the number of deviations from the mean for the limits using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{191.5-255.4}{63.9}= -1[/tex]
[tex] z=\frac{319.3-255.4}{63.9}= 1[/tex]
So we have values within 1 deviation from the mean and using the empirical rule we know that we have 68% of the values for this case
Bradley and Kelly are flying out kites at a park one afternoon. And model of Bradley and Kelly skates are shown Below on the coordinate plane as the kites BRAD and KELY, respectively:
Answer: b) they ARE similar because BRAD:KELY is 1:2
Step-by-step explanation:
In order for the shapes to be similar they must have congruent angles and proportional sides.
With the options a through d given, we can assume that their sides are proportional. Since BRAD is smaller than KELY, BRAD would have the smaller number in the ratio.
Answer:
They are similar because Brad and Kelly are 1:2
Step-by-step explanation:
Help me with this problem pleaseeeeee
Answer:
122 in2
Step-by-step explanation:
area = (2*tri area) + (3*rec area)
area = (2*0.5*4*3.5) + (3*4*9)
area = 14 + 108 = 122 Squared in
consider the exponential function f(x)= 1/5(15x) what is the value of the growth factor of the function?
Answer:
15
Step-by-step explanation:
The general form of an exponential equation is ...
f(x) = (initial value)(growth factor)^x
That is, the "growth factor" is the base of the exponent. In your equation ...
f(x) = (1/5)(15^x)
the growth factor is 15.
Answer:
D
Step-by-step explanation:
because you put the one and the five and BOOM the inter carol makes the wheel go round and round.
Sandy borrowed 6709R.O from a bank to buy a piece of land. If the bank charges 12 1/3 % compounded each two months, what amount will she have to pay after 2 years and half? Also find the interest
paid by her.
Answer:
Step-by-step explanation:
Using the compound interest formula
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
A = final amount after t years
P = amount borrowed = Principal = 6709R
r = rate (in %) = 12 1/3%
n = number of times the interest is applied = 2 months
t = time the period elapsed = 2 1/2 years
[tex]A = 6709(1+\frac{\frac{37}{300} }{\frac{2}{12} } )^{\frac{2}{12} *\frac{5}{2} } \\A = 6709(1+0.1233/0.1667)^{2\0.41667} \\A = 6709(1+0.7397)^{2\0.41667} \\A = 6709(1.7397)^{2\0.41667} \\A = 6709(3.81195)\\A = 25,574.373[/tex]
She will have to pay 25,574.373R after 2 and a half years
interest paid by her = Amount - Principal
Interest paid by her = 25,574.373 - 6709
Interest paid by her = 18,865.373R
A researcher is conducting a study on eating disorders. Using a list of recent participants in the online Weight Watchers program, she randomly selects a name from the alphabetized list. She then chooses every tenth person from that point on to include in her study. What is this sampling plan and example of?A. Judgmental SamplingB. Random SamplingC. Systematic SamplingD. Stratified SamplingE. Cluster Sampling
Answer:
Option c
Step-by-step explanation:
Systematic sampling is a probability type of samplng method in which elements are picked from a large population at a random start point and then the others are picked by constant periodic intervals which is usually done by dividing the population size by the chosen sample size. Then do a random start between 1 and the sampling interval, then repeatedly add the sampling interval to select subsequent elements.
In a study of the effectiveness of airbags in cars, 11,541 occupants were observed in car crashes with airbags available, and 41 of them were fatalities. Among 9,853 occupants in crashes with airbags not available, 52 were fatalities. (a) Construct a 95% confidence interval for the difference of the two population fatality rates. (please keep 4 decimal places throughout for accuracy) (b) Based on the confidence interval
Answer:
Please the read the answer below
Step-by-step explanation:
In order to find the 95% confidence interval for the difference of the two populations, you use the following formula (which is available when the population size is greater than 30):
CI = [tex](p_1-p_2)\pm Z_{\alpha/2}(\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}})[/tex] (1)
where:
p1: proportion of one population = 52/9853 = 0.0052
p2: proportion of the other population = 41/11541 = 0.0035
α: tail area = 1 - 0.95 = 0.05
Z_α/2: Z factor of normal distribution = Z_0.025 = 1.96
n1: sample of the first population = 52
n2: sample of the second population = 41
You replace the values of all parameters in the equation (1) :
[tex]CI =(0.0052-0.0035)\pm (1.96)(\sqrt{\frac{0.0052(1-0.0052)}{52}+\frac{0.0035(1-0.0035)}{41}})\\\\CI=0.0017\pm0.026[/tex]
By the result obtained in the solution, you can conclude that the sample is not enough, because the margin error is greater that the difference of proportion of each sample population.
Suppose that the function g is defined, for all real numbers, as follows.
Answer:
g(-5) = 2
g(0) = -2
g(1) = 2
Step-by-step explanation:
g(-5) satisfies x <-2, since -5 is less than -2.
g(0) satisfies -2≤x≤1 since 0 is greater than 2 but less than 1. When we plug in 0 into (x+1)^2 -2, we get -2.
g(1) satisfies -2≤x≤1 since it says that x is less than OR EQUAL TO 1. We then plug in 1 into (x+1)^2 -2 and get 2.
Which transformations of the graph of 1x) = -4*x result in the graph of f(x) = 4x+3?
First we need to take the - signal
So the difference between the graphs y = -4x and y = 4x is that they are mirrored by the y-axis
Now we have the graph y = 4x and want the graph y = 4x + 3
We just need to move the graph y = 4x 3 units to the left
So the transformations we need is to move it 3 units to the left and to mirror it by the y-axis
A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58. From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10. (a) Using the .01 level, what should the researcher conclude
Answer:
As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that listening to music while solving math problems will make a particular brain area more active.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=35\\\\H_a:\mu> 35[/tex]
The significance level is 0.01.
The sample has a size n=1.
The sample mean is M=58.
The standard deviation of the population is known and has a value of σ=10.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{1}}=10[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{58-35}{10}=\dfrac{23}{10}=2.3[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.3)=0.0107[/tex]
As the P-value (0.0107) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that listening to music while solving math problems will make a particular brain area more active.
Thirteen jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that 48% are of a minority race of the 13 jurors selected, 2 are
minores
(a) What proportion of the jury described is from a minority race?
(b) If 13 jurors are randomly selected from a population where 48% are minorities, what is the probability that 2 or fewer jurors will be minorities?
(c) What might the lawyer of a defendant from this minority race argue?
(a) The proportion of the jury described that is from a minority race is
(Round to two decimal places as needed)
(6) The probability that 2 or fewer out of 13 jurors are minorities, assuming that the proportion of the population that are minorities is 48%, is
(Round to four decimal places as needed.)
(c) Choose the correct answer below
O A The number of minorities on the jury is reasonable, given the composition of the population from which it came.
B. The number of minorities on the jury is impossible, given the composition of the population from which it came.
C. The number of minorities on the jury is unusually low, given the composition of the population from which it came.
OD. The number of minorities on the jury is unusually high, given the composition of the population from which it came
O O O
Answer:
a) The proportion of the jury described that is from a minority race is 0.15 or 15.38%, both to 2 d.p.
b) The probability that 2 or fewer out of 13 jurors are minorities, assuming that the proportion of the population that are minorities is 48%, is 0.0162
c) Option C is correct.
The lawyer of a defendant from this minority race should argue that
'The number of minorities on the jury is unusually low, given the composition of the population from which it came'.
Step-by-step explanation:
(a) What proportion of the jury described is from a minority race?
Of the 13 jurors, it is given in the question that only 2 of them are from a minority race.
Hence,
The proportion of the jury described that is from a minority race = (2/13) = 0.1538461538 = 0.154
(b) If 13 jurors are randomly selected from a population where 48% are minorities, what is the probability that 2 or fewer jurors will be minorities?
This problem is a binomial distribution problem
If X denotes the number of jurors that are from a minority race amongst the 13 jurors
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of jurors = 13
x = Number of successes required = 2 or fewer jurors = ≤ 2
p = probability of success = probability that a randomly picked member of the population as a juror is from a minority race = 48% = 0.48
q = probability of failure = probability that a randomly picked member of the population as a juror is NOT from a minority race = 1 - p = 1 - 0.48 = 0.52
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.00020325604 + 0.00243907252 + 0.01350870934
= 0.01615103791 = 0.0162 to 4 d.p.
(c) What might the lawyer of a defendant from this minority race argue?
Normally, the distribution of 13 jurors should reflect the population distribution with each race represented according to their population proportion or at least a proportion close to that.
But for this case, the proportion of the population from a minority race (48%) is more than 3 times the proportion of the jurors that are from a minority race (15.38%). This can introduce a very unfair bias in the decision of the jurors, hence, the lawyer of a defendant from this minority race might argue that the number of minorities on the jury is unusually low, given the composition of the population from which it came (less than ⅓).
Hope this Helps!!!
A normally distributed error term with mean of zero would Group of answer choices have values that are symmetric about the variance. allow more accurate modeling. yield biased regression estimates. be a hyperbolic curve.
Answer:
allow more accurate modeling
Step-by-step explanation:
They ask us what we should expect from a normally distributed error term with of zero, we analyze each option:
a. have values that are symmetric about the variance.
False, does not guarantee symmetry.
b. allow more accurate modeling.
It is correct, in this case we would have a more accurate model.
c. yield biased regression estimates.
it is also false, not necessarily.
d. be a hyperbolic curve.
false, not necessarily.
Use the multiplication rule for independent event probabilities. Two friends are both pregnant, and find out they are each expecting twins! Let A be the event that one friend is pregnant with identical twins, and note that P(A) = 0.0045. Let B be the event that the other friend is pregnant with fraternal twins, and note that P(B)= 0.01. A and B are independent events. What is the probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins? Give your answer as a percent, rounded to four decimal places if necessary.
Answer:
We have to multiply P(A) and P(B) which is 0.0045 * 0.01 * 100 (to make it a percentage) = 0.0045%.