Answer:
a. P ( X > 12 ) = 0.5254
b. P ( X < 15 ) = 0.7172
c. P ( 9 < X < 13 ) = 0.3179
d. Not unusual
Step-by-step explanation:
Solution:-
- We will define our random variable X as follows:
X: The weights of the male babies less than 2 month old in USA ( lb )
- The distribution given for the random variable ( X ) is defined to follow normal distribution.
- The normal distribution is identified by two parameters mean ( u ) and standard deviation ( σ ). The distribution is mathematically stated or expressed as:
X ~ Norm ( u , σ^2 )
- The parameters for the normal distribution followed by the random variable ( X ) are given. Hence,
X ~Norm ( 12.3 , 4.7^2 )
- We will use standard normal tables to determine the following probabilities:
a) What proportion of babies weigh more than 12 pounds?
- To use the standard normal tables we need to standardized our limiting value of the required probability by finding the corresponding Z-score value.
- The formula used to compute the Z-score value is given below:
[tex]Z-score = \frac{x - u}{sigma}[/tex]
- We are requested to compute the probability p ( X > 12 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z-score = \frac{12 - 12.3}{4.7} \\\\Z-score = -0.06382[/tex]
- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( X > 12 ) = P ( Z > -0.06382 ) = ...
P ( Z > -0.06382 ) = 1 - P ( Z < -0.06382 )
Use standard normal look-up table:
P ( X > 12 ) = 1 - 0.4746
P ( X > 12 ) = 0.5254 ... Answer
Answer: The proportion of babies that weigh more than 12 pounds is the probability of finding babies weighing more than 12 pounds among the total normally distributed population. The proportion is 0.5254
b) What proportion of babies weigh less than 15 pounds?
- We are requested to compute the probability p ( X < 15 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z-score = \frac{15-12.3}{4.7} \\\\Z-score = 0.57446[/tex]
- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( X < 15 ) = P ( Z < 0.57446 )
P ( X < 15 ) = 0.7172
Answer: The proportion of babies that weigh less than 15 pounds is the probability of finding babies weighing less than 15 pounds among the total normally distributed population. The proportion is 0.7172
c) What proportion of babies weigh between 9 and 13 pounds?
- We are requested to compute the probability p ( 9 < X < 13 ). the limiting value are 9 and 13 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z_1 = \frac{9-12.3}{4.7} = -0.70212\\\\Z_2 = \frac{13-12.3}{4.7} = 0.14893\\[/tex]
- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( 9 < X < 13 ) = P ( -0.70212 < X < 0.14893 )
P ( -0.70212 < X < 0.14893 ) = P ( X < 0.14893 ) - P ( X < -0.70212 )
Use standard normal look-up table:
P ( 9 < X < 13 ) = 0.5592 - 0.2413
P ( 9 < X < 13 ) = 0.3179 ... Answer
Answer: The proportion of babies that weigh less than 13 pounds but greater than 9 pounds is the probability of finding babies weighing less than 13 pounds and more than 9 pounds among the total normally distributed population. The proportion is 0.3179
d)
Is it unusual for a baby to weigh more than 18.1 pounds?
- We are requested to compute the probability p ( X > 18.1 ). the limiting value is 18.1 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z-score = \frac{18.1-12.3}{4.7} \\\\Z-score = 1.23404[/tex]
The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( X > 18.1 ) = P ( Z > 1.23404 )
P ( X > 18.1 ) = 0.1086
Answer: The proportion of babies that weight more than 18.1 pounds are 0.1086 of the total babies population. We can say that the proportion of babies that weigh more than 18.1 pounds are significant because the proportion lies is significant. Not enough statistical evidence to be classified as "unusual".
Find the first five terms in sequences with the following nth terms. 6n+3
Answer:
33
Step-by-step explanation:
An = 6n+3
so the first five terms in sequences is A5= 6*5 +3 = 33
if y varies inversely as the square of x, and when y = 4/63 find y when y varies inversely as the square of x = 3, and when find y when x=5
Answer:
Step-by-step explanation:
In order to solve this, we'll set up a proportion.
Since y is inversely related to the square of x, therefore:
y=4/63 ----->9 (square of x)
y=? ---------->25 (square of x)
According to the inverse relation:
y=4/63------->25
y=?------------->9 and y=4/175
Trish conducts an analysis which shows that the level of alcohol consumption affects reaction times more when a person is sleep-deprived than when a person is well-rested. This is an example of ______.
a. interaction
b. confounding
c. bias
d. main effect
Answer:
a. interaction
Step-by-step explanation:
In statistics, interaction occurs when the effect of one variable depends on the value of another variable.
In this case, Trish's analysis shows that the effect of alcohol consumption in a persons reaction time also depends on that person's quality of sleep, highlighting a clear case of interaction.
Given that the sum of the first n terms of the provided series is 6560 determine the value of n (2,6,18,54....)
Answer:
n = 8
Step-by-step explanation:
The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.
It has a common ratio of 3 => [tex] \frac{6}{2} = \frac{18}{6} = \frac{54}{18} = 3 [/tex]
Thus, the sum of the first n terms of a geometric sequence is given as [tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
Where,
[tex] a_1 [/tex] = first term of the series = 2
r = common ratio = 3
[tex] S_n [/tex] = sum of the first n terms = 6,560
Plug in the above values into the formula
[tex]6,560 = \frac{2(1 - 3^n)}{1 - 3}[/tex]
[tex] 6,560 = \frac{2(1 - 3^n)}{-2} [/tex]
[tex] 6,560 = \frac{1 - 3^n}{-1} [/tex]
Multiply both sides by -1
[tex] -6,560 = 1 - 3^n [/tex]
Subtract 1 from both sides
[tex] -6,560 - 1 = - 3^n [/tex]
[tex] -6,561 = - 3^n [/tex]
[tex] 6,561 = 3^n [/tex]
Evaluate
[tex] 3^8 = 3^n [/tex]
3 cancels 3
[tex] 8 = n [/tex]
The value of n = 8
Please answer this correctly without making mistakes
ANSWER :
Percentage = 50%
(if it odd and even then its 100%)
Answer:
100%
Step-by-step explanation:
There is a 100% chance rolling an odd or even since all the faces of this die are odd or even.
25e +-6e7 =
What the answer
Answer:
-6511.8
Step-by-step explanation:
Graph the system of linear equations.
-{ y = 4x+ 5 and y = 2x + 2.
Answer:
work shown and pictured
Last year, a soft drink manufacturer had 22% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 22% of the population will like the new soft drink. 1. Using α = .05, test to determine if more than 22% of the population will like the new soft drink. 2. What should be the critical value(s)? 3. If there is more than one, please enter the positive one. (please keep at least 4 digits after the decimal point).
Answer:
Critical value zc = 1.6449.
As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that more than 22% of the population will like the new soft drink.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22\\[/tex]
The significance level is 0.05.
The sample has a size n=400.
The sample proportion is p=0.25.
[tex]p=X/n=100/400=0.25[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{400}}\\\\\\ \sigma_p=\sqrt{0.000429}=0.0207[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.25-0.22-0.5/400}{0.0207}=\dfrac{0.0288}{0.0207}=1.3881[/tex]
As this is a right-tailed test, there is only one critical value and it is, for a significance level of 0.05, zc=1.6449.
As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.
Chase scored 14 points on Monday, and he doubled his score each day thereafter. How many points did he score on Thursday?
Answer:
112
Step-by-step explanation:
Original Score equals 14 right?
If chase doubles his original Score daily it will be
14*2 (Tuesday)=28
28×2 (Wednesday)=56
56×2 (Thursday)=112
Therefore,
Chase's Final score Equals 112
The number of points did he score on Thursday is 112.
Given that,
Chase scored 14 points on Monday. And he doubled his score each day thereafter.Based on the above information, the calculation is as follows:
On Monday = 14
On Tuesday = (14) (2) = 28
On Wednesday = (28) (2) = 56
On Thursday = (56) (2) = 112
Therefore, we can conclude that the number of points did he score on Thursday is 112.
Learn more: brainly.com/question/24169758
A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds.
A sample of seven infants is randomly selected, and their weights at birth are recorded as:
9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds.
If Alpha = 0.05,
1. What is the critical t-value?
2. What is the decision for a statistically significant change in average weights at birth at the 5% level of significance?
Answer:
1. Critical value t=±2.447
2. The null hypothesis is failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the birth weight significantly differs from 6.6 lbs.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=6.6\\\\H_a:\mu\neq 6.6[/tex]
The significance level is 0.05.
The sample has a size n=7.
The sample mean is M=7.56.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.18.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.18}{\sqrt{7}}=0.446[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.56-6.6}{0.446}=\dfrac{0.96}{0.446}=2.152[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=7-1=6[/tex]
For a two-tailed test with 5% level of significance and 6 degrees of freedom, the critical value for t is ±2.447.
As the test statistic t=2.152 is under 2.447 and over -2.447, it falls in the acceptance region, so the effect is not significant. The null hypothesis is failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.
Sample mean and standard deviation calculations:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{7}(9+7.3+6+. . .+6.6)\\\\\\M=\dfrac{52.9}{7}\\\\\\M=7.56\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{6}((9-7.56)^2+(7.3-7.56)^2+(6-7.56)^2+. . . +(6.6-7.56)^2)}\\\\\\s=\sqrt{\dfrac{8.32}{6}}\\\\\\s=\sqrt{1.39}=1.18\\\\\\[/tex]
If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is?
A. 33
B. 40
C. 49
D. 61
E. 84
Answer:
D
Step-by-step explanation:
3x, 4y, and 7z must be equal to the LCM of 3, 4, and 7 in order to be the smallest value. The LCM is 84 which means x = 28, y = 21 and z = 12. 28 + 21 + 12 = 61.
Answer:
61
Step-by-step explanation:
3x=4y=7z
x =4/3 y
x = 7/3 z
Since they have to be integers
y and z must be multiples of 3
y = 7/4 z
Since they have to be integers
z must be multiple of 4
Z must be a multiple of 12
Let z = 12
Then
y = 7/4 *12
y = 21
x = 7/3 *12
x = 28
x+y+z
28+ 21+12
61
Find the first four terms of the sequence defined by a(n subscript)= 1/n (separated by a comma).
Answer:
1,1/2,1/3,1/4
Step-by-step explanation:
an = 1/n
n is the term number
a1 = 1/1 =1
a2 = 1/2
a3= 1/3
a4 = 1/4
The first 4 terms are 1,1/2,1/3,1/4
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an equation to show the profit she will make on sneakers and sandals. P = [answer0]
Answer:
The equation that shows the profit: P = 2x + 3y
Step-by-step explanation:
The number of sneaker = x
The number of sandals = y
Cost of sneaker = 8 dollars.
Cost of sandals = 14 dollars.
Selling price of sneaker = $10
Selling price of sandals = $17
Total revenue = $10x + $17y
Total cost = $8x + $14y
Profit (P) = Total revenue - Total cost.
Profit = ($10x + $17y) – ($8x + $14y)
P = 10x +17y – 8x – 14y
P = 2x + 3y
Identify the axis of symmetry of the given quadratic
y= -3x^2 - 12
Answer:
[tex]\frac{d}{dy}(-3x^{2} -12) = -6x[/tex]
0 = -6x
0 = x
[tex]-3(0)^{2} -12 = -12[/tex]
(0,-12)
Step-by-step explanation:
6x^2-2x=20 use ac method
Answer:
Cannot be factored
Step-by-step explanation:
Need help with the problem 77
Hey there! :)
Answer:
∠A = 15.6°
Step-by-step explanation:
Use trigonometry to solve for ∠A. Since this involves the opposite and adjacent sides, tangent will be used. Therefore:
24/86 = arc tan x (inverse of tangent)
0.279 = arc tan x
x = 15.59° ≈ 15.6°.
Therefore:
∠A = 15.6°
For the functions f(x)=−9x^2+9 and g(x)=8x^2+9x, find (f+g)(x) and (f+g)(−1)
Answer:
f(x) = - 9x² + 9
g(x) = 8x² + 9x
To find (f+g)(x) add g(x) to f(x)
That's
(f+g)(x) = -9x² + 9 + 8x² + 9x
Group like terms
(f+g)(x) = - 9x² + 8x² + 9x + 9
(f+g)(x) = - x² + 9x + 9To find (f + g)(- 1) substitute - 1 into (f+g)(x)
That's
(f + g)(- 1) = -(-1)² + 9(-1) + 9
= - 1 - 9 + 9
= - 1Hope this helps you
2a -a + 1 =
x + y + x + 2 =
2(x + 4) + 2x =
3x + 2(x - 2) =
Answer:
Step-by-step explanation:
Please, share the instructions that come with each problem. Thanks.
2a -a + 1 = can be simplified to a + 1.
x + y + x + 2 = cannot be simplified.
2(x + 4) + 2x =
3x + 2(x - 2) = can be expanded and then simplified:
3x + 2x - 4 = 5x - 4
A student randomly guesses the answers to a 10 question true or false quiz. The observation in the student’s answer (T or F) for each question. Describe the sample space
Answer:
in this experiment we only have two sample space which is only true or false.
because all the answers will have to fall between this sample space.
Step-by-step explanation:
we cannot actually or fully understand the above answer without first of all defining or explaining what sample space actually means.
Sample space: this is the set of all possible outcome that may come from an experiment.or we can say simply say it is the range of values that the experiment depends on.
Less than 51% of workers got their job through networking. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0 : p H1 : p
Use the following codes to enter the following symbols:
≥≥ enter >=
≤≤ enter <=
≠≠ enter !=
Answer:
Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Step-by-step explanation:
We are given that less than 51% of workers got their job through networking. We have to express the null and alternative hypotheses in symbolic form for this claim.
Let p = population proportion of workers who got their job through networking
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Here, the null hypothesis states that greater than or equal to 51% of workers got their job through networking.
On the other hand, the alternate hypothesis states that less than 51% of workers got their job through networking.
Hence, this is the appropriate hypothesis that can be used.
Can someone help with this I can't fail.
Answer: B
Step-by-step explanation:
(f-g)(x) is f(x)-g(x). Since we have f(x) and g(x), we can directly subtract them.
5x-2-(2x+1) [distribute -1]
5x-2-2x-1 [combine like terms]
3x-3
Management at a home improvement store randomly selected 95 customers and observed their shopping habits.They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store.
a. number of items-discrete: total time-discrete
b. number of items-continuous; total time-discrete
c. number of items-continuous; total time-continuous
d. number of items-discrete; total time-continuous
Answer:
d. number of items-discrete; total time-continuous
Step-by-step explanation:
Continuous:
Real numbers, can be integer, decimal, etc.
Discrete:
Only integer(countable values). So can be 0,1,2...
In this question:
You can purchase 0, 1, 2,...,10,...,100,... items, so the number of items is discrete.
You can spend for example, 0.5 hours in the store, or 2.5 minutes, that is, can be decimal numbers. So the total time is continuous
The correct answer is:
d. number of items-discrete; total time-continuous
A sum lent out at simple interest becomes rs4480 in 3 years and rs 4800 in 5years.find the rate of interest
Answer: rate = 4%
Step-by-step explanation:
SI = 4800 - 4480 = 320 for two years
For 1 year, it is 320/2 = 160
For 5 years, it is 160 * 5 = 800
Principal = Amount -SI
P = 4800 - 800 = 4000
SI = prt / 100
800 = (4000 * r * 5) / 1000
r = 800 * 100 / 4000 * 5
r = 4%
Answer:
Rate of intrest = 4%
Step-by-step explanation:
Short forms
Simple intrest=SI Year= Y Rate= r
SI= 4800-4480
= 320
1 year= 320/2 = 160
5year= 160 x 5
= 800
P= Amount-SI
P= 4800-800
= 4000
SI=PRT/100
800=(4000 X r X 5)/1000
r=800 x 100/4000 x 5
r= 4%
Hope it was Helpful!
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In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The
longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox.
In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function
to model the hours of daylight hours on certain days of the year in New York City.
Identify the independent and dependent variables find amplitude and the period of the function create a trigonometric function that describes the hours of sunlight for each day of the year and then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
independent: day number; dependent: hours of daylight
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
1.79 fewer hours on Feb 10
Step-by-step explanation:
a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).
__
b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,
March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...
d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
__
c) d(41) = 10.34, so February 10 will have ...
12.13 -10.34 = 1.79
hours less daylight.
You are walking directly away from your house. You are 555 miles away from your house when you start walking, so you can determine your distance from your house by adding 555 to the number of miles you have walked. In the equation below, xxx represents the number of miles you have walked, and yyy represents your distance from home in miles. The relationship between these two variables can be expressed by the following equation: y=x+5y=x+5y, equals, x, plus, 5 Identify the dependent and independent variables. Dependent variable Independent variable Your distance from home Number of miles you walk
Answer:
Dependent variable is Your distance from home(y)Independent variable is Number of miles you walk(x)Step-by-step explanation:
x represents the number of miles you have walked
y represents your distance from home in miles.
The relationship between these two variables can be expressed by the following equation: y=x+5
The dependent variable is that whose value changes whenever the value of the independent variable is changed.
From the equation above:
When x=1, y=1+5=6 milesWhen x=3, y=3+5=8 milesWe can clearly see that y changes for different values of x.
Therefore:
Dependent variable is Your distance from home(y)Independent variable is Number of miles you walk(x)Answer:
1dependant
2independant
Step-by-step explanation:
Mr. Rosenberger asked his students to use the distributive property to rewrite the expression 18 (24) by using friendlier numbers. The table below shows the expressions that four students created. Expressions Created by Students Student Expression Aaron 10 + 8 times 4 + 20 Brian 10 + 8 (4 + 20) Cece 18 (4 + 6) Diana 18 (4 + 20)
Answer:
diana
Step-by-step explanation:
Answer:
I think it’s Diana I’m sorry if I’m wrong :P
When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. How y’all is a person if he casts a 1.5 foot shadow at the same time?
Answer:
6 ft
Step-by-step explanation:
The building height of 100 ft is 4 times the shadow length of 25 ft. At the same ratio, the person's height is 4 times the 1.5 ft shadow length, so is ...
4 × (1.5 ft) = 6.0 ft
The person is 6 ft tall.
Need help with this question thanks!
A department store finds that in a random sample of 200 customers, 60% of the sampled customers had browsed its website prior to visiting the store. Based on this data, a 90% confidence interval for the population proportion of customers that browse the store’s website prior to visiting the store will be between
Answer:
between 108-110?
Step-by-step explanation:
60% or 200 = 120 people
90% of 120 = 108
question doesnt look complete so this is the best I could come up with...♀️
What is the constant of proportionality in the equation Y = x/9?
Answer:
1/9
Step-by-step explanation:
Separate the fraction (1/9) from the variable x:
y = (1/9)x.
1/9 is the constant of proportionality.