Mathematics, 06.05.2020 18:03 lightskinbaby2

An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample.

a. what is the standard error of the mean in this experiment?

b. what is the probability that the sample mean is between $3.78 and $3.86?

c. what is the probability that the difference between the sample mean and the population mean is less than $0.01?

d. what is the likelihood the sample mean is greater than $3.92?

Answers: 1

Show answers

Answers

Answer from: gursparks

(a) The standard error of the mean in this experiment is $0.052.

(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The information provided is:

$n=40\\\mu=\$3.82\\\sigma=\$0.33$

As n = 40 > 30, the distribution of sample mean is $\bar X\sim N(3.82,\ 0.052^{2})$ .

(a)

The standard error is the standard deviation of the sampling distribution of sample mean.

Compute the standard deviation of the sampling distribution of sample mean as follows:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

$=\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052$

Thus, the standard error of the mean in this experiment is $0.052.

(b)

Compute the probability that the sample mean is between $3.78 and $3.86 as follows:

P(3.78

=P(-0.77

Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c)

If the difference between the sample mean and the population mean is less than $0.01 then:

$\bar X-\mu_{\bar x}$

Compute the value of $P(\bar X$ as follows:

$P(\bar X$

=P(Z

Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d)

Compute the probability that the sample mean is greater than $3.92 as follows:

$P(\bar X3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}\frac{3.92-3.82}{0.052})$

=P(Z

Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.

Answer from: Quest

three-fourths of an hour

36÷48=0.75

0.75= $\frac{3}{4}$

Answer from: Quest

it has the same slope and a different y-intercept

hope this : )

Another question on Mathematics

Mathematics, 21.06.2019 18:30

Icould really use some with this question.

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

The graph and table shows the relationship between y, the number of words jean has typed for her essay and x, the number of minutes she has been typing on the computer. according to the line of best fit, about how many words will jean have typed when she completes 60 minutes of typing? 2,500 2,750 3,000 3,250

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

The equation shown below represents function f. f(x)= -2x+5 the graph shown below represents function g. which of the following statements is true? a. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is less than the y-intercept of function g. b. over the interval [2, 4], the average rate of change of f is greater than the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. c. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. d. over the interval [2, 4], the average rate of change of f is less than the average rate of change of g. the y-intercept of function f is the same as the y-intercept of function g.

Answers: 1

Answer

Mathematics, 21.06.2019 23:40

The frequency table shows the results of a survey asking people how many hours they spend online per week. on a piece of paper, draw a histogram to represent the data. then determine which answer choice matches the histogram you drew. in order here is the.. hours online: 0-3, 4-7, 8-11, 12-15, and 16-19. frequency: 5, 8, 10, 8, 7 answer for the question is in the picture! : )

Answers: 2

Answer

You know the right answer?

An economist uses the price of a gallon of milk as a measure of inflation. She finds that the averag...

Questions