Answer:
The probability that exactly 4 don't grow is P=0.0287.
Step-by-step explanation:
This random variable can be modeled with a binomial distribution.
The sample size is n=7, the total amount of seeds planted.
The probability of success is p=0.8.
The probability that k seeds grow in the sample is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{7}{k} 0.8^{k} 0.2^{7-k}\\\\\\[/tex]
If exactly 4 don't grow, this means that exactly 7-4=3 seeds grow.
Then, we have to calculate P(x=3):
[tex]P(x=3) = \dbinom{7}{3} 0.8^{3}\cdot 0.2^{4}=35*0.512*0.0016=0.0287\\\\\\[/tex]
One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?
20 points if you can answer in under 30 minuets
Answer:
x=5 x=-3
Step-by-step explanation:
x^2 − 2x − 15 =0
Factor
What two numbers multiply to -15 and add to -2
-5*3 = -15
-5+3 =-2
(x-5) (x+3)=0
Using the zero product property
x-5 =0 x+3 =0
x=5 x=-3
Answer:
x^2 - 2x - 15 = 0
(x - 5) (x + 3) = 0
x - 5 = 0
x = 5
x + 3 = 0
x = -3
g A researcher is interested in whether people are able to identify emotions correctly when they are extremely tired. It is known that, using a particular method of measurement, the accuracy ratings of people in the general population (who are not extremely tired) are normally distributed with a mean of 82 and a variance of 20. In the present study, the researcher arranges to test 50 people who had not slept the previous night. The researcher predicts that these people will have different accuracy than the general population, but does not predict a direction. The mean accuracy for these 50 individuals was a 78. Using the .05 level of significance, what should the researcher conclude
Answer:
The researcher can conclude that the mean is not 82. i.e. the people will have different accuracy than the general population.
Step-by-step explanation:
mean, [tex]\mu = 82[/tex]
Variance, v = 20
Sample size, n = 50
Standard deviation, [tex]\sigma = \sqrt{20} = 4.4721[/tex]
Sample mean, [tex]\bar{X} = 78[/tex]
Level of significance, [tex]\alpha = 0.05[/tex]
Null hypothesis, [tex]H_o: \mu = 82\\[/tex]
Alternative hypothesis, [tex]H_a: \mu \neq 82[/tex]
Calculate the test statistics:
[tex]z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n} } \\\\z = \frac{78 - 82}{4.4721\sqrt{50} }\\\\z = - 6.32[/tex]
Get the critical value of z at 5% significant level:
[tex]z_{crit} = \pm 1.96[/tex]
Since the test statistics is less than the critical values of z, the null hypothesis is rejected.
For the functions f(x)=3x−1 and g(x)=4x−3, find (f∘g)(x) and (g∘f)(x)
When a frequency distribution is exhaustive, each individual, object, or measurement from a sample or population must appear in at least one category.
a. True
b. False
Answer:
a. True
Step-by-step explanation:
The frequency distribution is a summary of the gathered data set, in which the interval of values is divided into classes.
A requirement for a frequency distribution is for the classes to be mutually exclusive and exhaustive. That is, each individual, object, or measurement in the data set must belong to one and only one class.
Then, we can conclude that each individual, object, or measurement must appear in at least one (in fact, only in one) category or class.
Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What are the minimum value of the bill that is greater than 95% of the bills?
Answer:
The minimum value of the bill that is greater than 95% of the bills is $37.87.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 28, \sigma = 6[/tex]
What are the minimum value of the bill that is greater than 95% of the bills?
This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 28}{6}[/tex]
[tex]X - 28 = 6*1.645[/tex]
[tex]X = 37.87[/tex]
The minimum value of the bill that is greater than 95% of the bills is $37.87.
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2 days. What is the probability of spending between 4 and 7 days in recovery? (Round your answer to four decimal places.)
Answer:
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = 0.5445
Step-by-step explanation:
Step(i):-
Given mean of the Population μ = 5.3 days
Given standard deviation of the population 'σ' = 2 days
Let 'X' be the random variable in normal distribution
Let x₁ = 4
[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{4-5.3}{2} = -0.65[/tex]
Let x₂ = 7
[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{7-5.3}{2} = 0.85[/tex]
Step(ii):-
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = P(-0.65≤Z≤0.85)
= P(Z≤0.85) - P(Z≤-0.65)
= 0.5 + A( 0.85) - ( 0.5 - A(-0.65)
= 0.5 + A( 0.85) - 0.5 +A(0.65) ( ∵A(-0.65) = A(0.65)
= A(0.85) + A(0.65)
= 0.3023 + 0.2422
= 0.5445
Final answer:-
The probability of spending between 4 and 7 days in recovery
P(4≤x≤7) = 0.5445
20. Evaluate:
(55.5 x 2) = 5 + 13-7
Answer: 111=11
Step-by-step explanation: PEMDAS
(55.5 times 2)=5+13-7
(111)=5+13-7
(111)=18-7
111=11
If f(x) = 3x2 − 8x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.
Split up the interval [0, 3] into 6 subintervals,
[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]
The right endpoints are given by the arithmetic sequence,
[tex]r_i=0+\dfrac i2=\dfrac i2[/tex]
with [tex]1\le i\le6[/tex].
We approximate the integral of [tex]f(x)[/tex] on the interval [0, 3] by the Riemann sum,
[tex]\displaystyle\int_0^3f(x)\,\mathrm dx=\sum_{i=1}^6f(r_i)\Delta x_i[/tex]
[tex]\displaystyle=\frac{3-0}6\sum_{i=1}^6\left(3{r_i}^2-8r_i\right)[/tex]
[tex]\displaystyle=\frac12\sum_{i=1}^6\left(\frac{3i^2}4-4i\right)[/tex]
[tex]\displaystyle=\frac38\sum_{i=1}^6i^2-2\sum_{i=1}^6i[/tex]
Recall the formulas,
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6[/tex]
Then the value of the integral is approximately
[tex]\displaystyle=\frac38\cdot\frac{6\cdot7\cdot13}6-2\cdot\frac{6\cdot7}2=\boxed{-\frac{63}8}=-7.875[/tex]
Compare to the exact value of the integral, -9.
The Riemann sum of [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex] with [tex]n = 6[/tex] is [tex]-\frac{63}{8}[/tex].
The formula for the right Riemann sum is described below:
[tex]S = \frac{b-a}{n} \cdot \Sigma\limit_{i= 1}^{n} \,f(x+i\cdot \frac{b-a}{n} )[/tex] (1)
Where:
[tex]S[/tex] - Riemann sum.[tex]a[/tex] - Lower bound.[tex]b[/tex] - Upper bound.[tex]n[/tex] - Number of segments.[tex]i[/tex] - Segment index.If we know that [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex], [tex]a = 0[/tex], [tex]b = 3[/tex] and [tex]n = 6[/tex], then the Riemann sum is:
[tex]S = \frac{3-0}{6}\cdot [f(0.5) + f(1) + f(1.5) + f(2) + f(2.5) +f(3)][/tex]
[tex]S = \frac{1}{2}\cdot \left(-\frac{13}{4}-5-\frac{21}{4}-4-\frac{5}{4}+3\right)[/tex]
[tex]S = -\frac{63}{8}[/tex]
The Riemann sum of [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex] with [tex]n = 6[/tex] is [tex]-\frac{63}{8}[/tex].
We kindly invite to check this question on Riemann sum: https://brainly.com/question/23960718
A pizza chain plans to locate a new pizza franchise on the CCSU campus if the results of a survey show that more than 10% of CCSU students would eat there at least once a week. Suppose the company is about to carry out a hypothesis test. 7.
a. State the hypotheses.
b. Clearly state, in terms of this particular problem, what a Type I error would mean.
c. Describe possible consequences of a Type I error in this situation.
d. Clearly state, in terms of this particular problem, what a Type II error would mean.
e. Describe possible consequences of a Type II error in this situation.
Answer:
a) Null and alternative hypothesis:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.
c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.
d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%
e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.
Step-by-step explanation:
a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.
Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.
On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.
This can be written as:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
solve for z.
z/12 < 3
Answer: z < 36
Step-by-step explanation: To solve for z in this inequality, we multiply by 12 on both sides of the inequality to get z < 36.
We can write this in set notation as {z: z < 36}.
━━━━━━━☆☆━━━━━━━
▹ Answer
z < 36
▹ Step-by-Step Explanation
[tex]\frac{z}{12} < 3\\\\12 * \frac{z}{12} < 12 * 3\\\\z < 12 * 3\\\\z < 36[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
A pencil consists of a cone stacked on top of a cylinder. The diameter of the cylindrical base of the pencil is 10 mm and the height of the cylinder is 70 mm, while the height of the cone is 12 mm. Calculate the surface area of the pencil. Leave your answer in terms of π. 835π sq. mm. 790π sq. mm. 785π sq. mm. 1820π sq. mm.
Answer:
790π
Step-by-step explanation:
We are given;
Diameter of cylinder;d = 10 mm
So, radius;r = 10/2 = 5 mm
Height of cylinder;h = 70mm
Surface area of cylinder is given by the formula; S.A = 2πr² + 2πrh
Plugging in the relevant values, we have;S.A = 2π(5)² + 2π(5)(70)
S.A = 50π + 700π
S.A = 750π
Now, because one base of the cylinder is hidden as the cone is stacked on that face, we will deduct the area of that base face;
Thus, Surface area = 750π - π(5)² = 750π - 25π = 725π
For the cone,
Height;h = 12mm
Since this is stacked directly on the cylinder, it will have the same radius. Thus; radius;r = 5mm
Now,formula for surface area of cone is;
S.A = πr² + πrL
Where L is slant height.
We can use pythagoras theorem to get L.
So, L² = r² + h²
L = √r² + h²
L = √(5² + 12²)
L = √(25 + 144)
L = √169
L = 13
So, S.A of cone = π(5)² + (π×5×13)
S.A = 25π + 65π = 90π
Similar to what was done to the Cylinder, since the circular base of the cone is stacked on the cylinder, we will deduct the surface area of that base as it is hidden.
So, S.A is now = 90π - π(5)²
= 90π - 25π = 65π
Thus,total surface area of the pencil = 725π + 65π = 790π
Answer:[tex]790\pi sq. Mm[/tex]
Step-by-step explanation:got it right on the test
(2.8(2 4/5 ·(8.75−2 1/2 )))·7.25−3 3/4
Answer:
351.5
Step-by-step explanation:
Step 1: Convert fractions to improper
(2.8(14/5(8.75 - 5/2)))7.25 - 15/4
Step 2: Parenthesis
(2.8(14/5(6.25)))7.25 - 15/4
Step 3: Parenthesis
(2.8(17.5))7.25 - 15/4
Step 4: Parenthesis
49(7.25) - 15/4
Step 5: Multiply
355.25 - 15/4
Step 6: Subtract
351.5
What is the measure of angle ABC?
Answer:
88
Step-by-step explanation:
Angle Formed by Two Chords = 1/2( sum of Intercepted Arcs)
ABD = 1/2 ( 131+ 53)
ABD = 1/2 (184)
=92
We know that ABC + ABD form a straight line
ABC = 180 -ABD
ABC = 180 -92
ABC = 88
Use the graphing calculator to graph the line y = 2x – 7.
Use the graph to find the missing coordinates below.
(4.75, )
(, –7.7)
(0.4, )
Answer:
(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)
Step-by-step explanation:
Given the line
[tex]y = 2x- 7[/tex]
Given the missing coordinates:
(4.75, )
(, –7.7)
(0.4, )
We know that every coordinate is of the form [tex](x,y)[/tex].
So, we can easily solve the for other variable if one variable is given from the given line using the graph or the given equation.
For the first coordinate:
(4.75, )
From graph it can be found that y = 2.5
Verifying using the equation.
Putting the value of x = 4.75 in the equation we get:
y = 2[tex]\times[/tex] 4.75 - 7
y = 9.5 - 7 = 2.5
So, the coordinate is (4.75, 2.5)
For the second coordinate:
(, -7.7 )
From graph it can be found that x = -0.35
Verifying using the equation:
Putting the value of y = -7.7 in the equation we get:
-7.7 = 2x - 7
2x = -7.7 + 7 = -0.7
x = -0.35
So, the coordinate is (-0.35, -7.7).
For the third coordinate:
(0.4, )
From graph it can be found that y = -6.2
Verifying using the equation.
Putting the value of x = 0.4 in the equation we get:
y = 2[tex]\times[/tex] 0.4 - 7
y = 0.8 - 7 = -6.2
So, the coordinate is (0.4, -6.2)
Also, please refer to the attached graph.
So, the answer is:
(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)
Answer: its 2.5, -0.35, -6.2
Step-by-step explanation: in easier words
A survey was conducted to find out how many people use public transportation to get to work. The results for 4625 respondents are broken down by gender: 1000 of 2570 males and 1532 of 2055 females use public transportation every working day. Use the information to find the standard error for the difference in proportions of males and females who use public transportation every working day and check the conditions for a normal distribution.
Answer:
The standard error for the difference in proportions of males and females who use public transportation every working day is 0.015.
The conditions are met.
Step-by-step explanation:
The sample 1 (males), of size n1=2570 has a proportion of p1=0.389.
[tex]p_1=X_1/n_1=1000/2570=0.389[/tex]
The sample 2 (females), of size n2=2055 has a proportion of p2=0.745.
[tex]p_2=X_2/n_2=1532/2055=0.745[/tex]
The difference between proportions is (p1-p2)=-0.356.
[tex]p_d=p_1-p_2=0.389-0.745=-0.356[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{1000+1532}{2570+2055}=\dfrac{2532}{4625}=0.547[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.547*0.453}{2570}+\dfrac{0.547*0.453}{2055}}\\\\\\s_{p1-p2}=\sqrt{0.000096+0.000121}=\sqrt{0.000217}=0.015[/tex]
Conditions for a normal distribution approximation:
The expected number of "failures" or "successes", whichever is smaller, has to be larger than 10.
For the males sample, we have p=0.389 and (1-p)=0.611. The sample size is n=2570, so we take the smallest proportion and chek the condition:
[tex]n\cdot p=2570\cdot 0.389=999>10[/tex]
For the females sample, we have p=0.745 and (1-p)=0.255. The sample size is n=2055, so we take the smallest proportion and chek the condition:
[tex]n\cdot (1-p)=2055\cdot 0.255=524>10[/tex]
The conditions are met.
Abigail and Liza Work as carpenters for different companies Abigail earns $20 Per hour at her company and Liza Word for a total of 30 hours in together earned a total of 690 how many hours did Liza work last week?
This question was not properly written, hence it is incomplete. The complete question is written below:
Complete Question:
Abigail and Liza work as carpenters for different companies. Abigail earns $20 per hour at her company and Liza earns $25 per hour at her company. Last week, Abigail and Liza worked for a total of 30 hours and together earned a total of $690. How many hours did Liza work last week?
Answer:
Lisa worked for 18 hours last week
Step-by-step explanation:
Let the number of hours Abigail worked last week = A
Let the number of hours Liza worked last week = B
Abigail earns = $20 per hour at her company
Liza earns = $25 per hour at her company
A + B = 30 ........... Equation 1
B = 30 - A
20 × A + 25 × B = 690
20A + 25B = 690 ............... Equation 2
Substitute 30 - A for B in Equation 2
Hence, we have:
20A + 25(30 - A) = 690
20A + 750 - 25A = 690
Collect like terms
20A - 25A = 690 - 750
-5A = -60
A = -60/-5
A = 12
Since A represents the number of hours Abigail worked, Abigail worked for 12 hours last week.
Substitute 12 for A in Equation 1
A + B = 30
12 + B = 30
B = 30 - 12
B = 18
Since B represents the number of hours Liza worked, therefore, Liza worked for 18 hours last week.
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03
Answer:
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 0.03?
This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So
X = 0.08
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.02
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Anita works at a local news station and needs to decide which news story to report first. Of the news stories, 3 are local, 4 are international, and 5 national. The stories are equally important so anita randomly orders the stories. What is the probability that the first story is a national story. Give your answer as a fraction
what is the solution for the inequality l2x-6l<4
Answer:
x < 5 or x > 1
Step-by-step explanation:
2x - 6 < 4
2x < 4 + 6
2x < 10
x < 10/2
x < 5
2x - 6 > - 4
2x > - 4 + 6
2x > 2
x > 2/2
x > 1
About ____% of the area is between z= -2 and z= 2 (or within 2 standard deviations of the mean)
Answer:
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Step-by-step explanation:
Explanation:-
Given data Z = -2 and Z =2
The probability that
P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)
= 0.5 + A(2) - ( 0.5 - A(-2))
= A (2) + A(-2)
= 2 × A(2) (∵ A(-2) = A(2)
= 2×0.4772
= 0.9544
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x)=_________
Answer:
Terms:
1) = 7/3
2) = -7/9
3) = 7/27
4) = -7/81
Step-by-step explanation:
Your question did not state the equation of f(x), however; assuming f(x) = 7/(1+x) ,....... at a = 2
see solution attached then use it to work your f(x)
You want to determine the percentage of seniors who drive to campus. You take a random sample of 125 seniors and ask them if they drive to campus. Your 95% confidence interval turns out to be from 0.69 to 0.85. Select each correct interpretation of this situation. There might be no, one, or more than one correct statement. Explain, the reason if it is not a correct interpretation.
Answer:
The statements that are true are: A, B, F, G, and H.
Step-by-step explanation:
The statements are:
A. A 90% confidence interval would be narrower than the interval given.
TRUE.
The less confidence, the less conservative is the interval and the narrower it can be. So this statement is true.
B. You are 95% confident that the proportion of all seniors who drive to campus is in the interval from .69 to .85.
TRUE.
That is the definition of confidence interval.
C. 95% of all seniors drive to campus from 69% to 85% of the time, and the rest drive more frequently or less frequently.
FALSE.
The confidence interval only has meaning referred to the population proportion, not the individual values. So we can not claim this is true.
D. All seniors drive to campus an average of 77% of the time.
FALSE.
The average is expected to be, with 95% confidence, between 0.69 and 0.85. The sample proportion is 0.77*, and this outcome is used to calculate the confidence interval, but we don't know if the true average is 0.77.
*Sample proportion:
[tex]p=(LL+UL)/2=(0.69+0.85)/2=1.54/2=0.77[/tex]
E. You are 95% confident that the proportion of seniors in the sample who drive to campus is between .69 and .85.
FALSE.
The sample proportion is known and it is 0.77.
F. 77% of the seniors in your sample drive to campus.
TRUE.
This is the sample proportion.
G. If the sampling were repeated many times, you would expect 95% of the resulting samples to have a sample proportion that falls in the interval from .69 to .85.
TRUE.
This is a property of the confidence intervals.
H. If the sampling were repeated many times, you would expect 95% of the resulting confidence intervals to contain the proportion of all seniors who drive to campus.
TRUE.
This is a property of the confidence intervals.
A building society offers a rate of 11% per annum simple interest. Beth-Ann deposit 24000 in the society for 15 months. Calculate the amount of money due to her at the end of this period
Answer:
The amount of money due to Beth-Ann at the end of this period is $27, 300.
Step-by-step explanation:
The amount at the end of a period, when simple interest is being charged is:
Amount (A) = Principal (P) + Interest (I)
Here interest is computed using the formula:
[tex]I=P\times R\times T[/tex]
It is provided that:
P = 24,000
R = 11%
T = 15 months = 1.25 years
Compute the Interest as follows:
[tex]I=P\times R\times T[/tex]
[tex]=24000\times 0.11\times 1.25\\=3300[/tex]
The interest earned is, I = $3,300.
Compute the amount of money due to Beth-Ann at the end of this period as follows:
[tex]A=P+I[/tex]
[tex]=24000+3300\\=27300[/tex]
Thus, the amount of money due to Beth-Ann at the end of this period is $27, 300.
A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a -credit course, a B in each of -credit courses, a C in a -credit course, and a D in a -credit course?
Question Correction
One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, 1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 3-credit course, a B in each of three 4-credit courses, a C in a 2-credit course, and a D in a 3-credit course?
Answer:
2.75
Step-by-step explanation:
We present the information in the table below.
[tex]\left|\begin{array}{c|c|c|c}$Course Grade&$Grade Point(x)&$Course Credit(y)&$Product(xy)\\---&---&---&---\\A&4&3&12\\B&3&4&12\\B&3&4&12\\B&3&4&12\\C&2&2&4\\D&1&3&3\\---&---&---&---\\$Total&&20&55\end{array}\right|[/tex]
Therefore, the GPA of the student is:
[tex]GPA=\dfrac{55}{20}\\\\ =2.75[/tex]
After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.
a.â Let X =1 if successful, X= 0 if not. Find the mean and variance of X.
b.â If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.
c.â Find the mean and variance of Y.
Answer:
a) Mean of X = 0.40
Variance of X = 0.24
b) Y is a Bernoulli's distribution. Check Explanation for reasons.
c) Mean of Y = 0.80 points
Variance of Y = 0.96
Step-by-step explanation:
a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.
Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.
The probability mass function of X is then
X | Probability of X
0 | 0.60
1 | 0.40
The mean is given in terms of the expected value, which is expressed as
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40
Variance = Var(X) = Σx²p − μ²
μ = mean = E(X) = 0.40
Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40
Variance = Var(X) = 0.40 - 0.40² = 0.24
b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.
A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).
Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.
The probability mass function for Y is then
Y | Probability of Y
0 | 0.60
2 | 0.40
c) Mean and Variance of Y
Mean = E(Y)
E(Y) = Σ yᵢpᵢ
yᵢ = each variable
pᵢ = probability of each variable
E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points
Variance = Var(Y) = Σy²p − μ²
μ = mean = E(Y) = 0.80
Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60
Variance = Var(Y) = 1.60 - 0.80² = 0.96
Hope this Helps!!!
What the sum for (50+11)*(8p-4)
Answer:
488p - 244
Step-by-step explanation:
Step 1: Add
61(8p - 4)
Step 2: Distribute
488p - 244
The height of a certain plant is determined by a dominant allele T corresponding to tall plants, and a recessive allele t corresponding to short (or
dwarf) plants. If both parent plants have genotype Tt, compute the probability that the offspring plants will be tall. Hint: Draw a Punnett square.
(Enter your probability as a fraction.)
Answer:
The probability of the plants being tall is equal to P(TT) + P(Tt)= 1/4+1/2=3/4
Step-by-step explanation:
Hello!
The characteristic "height" of a plant is determined by the alleles "tall" T (dominant) and "short" a (recessive). If both parents are Tt, you have to calculate the probability of the offspring being tall (TT or Tt)
To construct the Punnet square you have to make a table, where the parental alleles will be in the margins, for example: the father's alleles in the columns and the mother's alleles in the rows.
Each parent will produce a haploid gamete that will carry one of the alleles, so the probability for the offspring receiving one of the alleles is 1/2
Father (Tt): gametes will carry either the dominant allele T or the recessive allele t with equal probability 1/2
Mother (Tt): gametes will also carry either the dominant allele T or the recessive allele t with equal probability 1/2
Then you have to cross each allele to determine all possible outcomes for the offsprings. For each cell, the probability of obtaining both alleles will be the product of the probability of each allele (See attachment)
First combination, the offspring will receive one dominant allele from his father and one dominant allele from his mother: TT, the probability of obtaining an offspring with this genotype will be P(T) * P(T) = 1/2*1/2=1/4
Second combination, the offspring will receive the recessive allele from the father and the dominant allele from the mother, then its genotype till be tT with probability: P(t)*P(T)= 1/2*1/2=1/4
Third combination, the offspring will receive one dominant allele from his father and one recessive allele from his mother, the resulting genotype will be Tt with probability: P(T)*P(t)= 1/2*1/2=1/4
Combination, the offspring will receive both recessive alleles from his parents, the resulting genotype will be tt with probability: P(t)*P(t)= 1/2*1/2=1/4
So there are three possible genotypes for the next generation:
TT with probability P(TT)= 1/4
Tt with probability: P(Tt)+P(tT)=1/4+1/4=1/2⇒ This genotype is observed twice so you have to add them.
tt with probability P(tt)= 1/4
Assuming this genotype shows complete dominance, you'll observe the characteristic "Tall" in individuals that carry the dominant allele "T", i.e. individuals with genotype "TT" and "Tt"
So the probability of the plants being tall is equal to P(TT) + P(Tt)= 1/4+1/2=3/4
I hope this helps!
the required condition for using an anova procedure on data from several populations for mean comparison is that the
Answer:
The sampled populations have equal variances
Step-by-step explanation:
ANOVA which is fully known as Analysis of variances can be defined as the collection of statistical models as well as their associated estimation procedures which enables easily and effectively analyzis of the differences among various group means in a sample reason been that ANOVA is a total variance in which the observed variance in a specific variable is been separated into components which are attributable to various sources of variation which is why ANOVA help to provides a statistical test to check whether two or more population means are equal.
Therefore the required condition for using an ANOVA procedure on data from several populations for mean comparison is that THE SAMPLED POPULATION HAVE EQUAL VARIANCE.