Question

Suppose that we will randomly select a sample of 79 measurements from a population having a...

Suppose that we will randomly select a sample of 79 measurements from a population having a mean equal to 21 and a standard deviation equal to 8. (a) Describe the shape of the sampling distribution of the sample mean . Do we need to make any assumptions about the shape of the population? Why or why not? Normally distributed ; yes , because the sample size is large . (b) Find the mean and the standard deviation of the sampling distribution of the sample mean . (Round your σx¯ answer to 1 decimal place.) µ 21 σ 0.9 (c) Calculate the probability that we will obtain a sample mean greater than 23; that is, calculate P( > 23). Hint: Find the z value corresponding to 23 by using µ and σ because we wish to calculate a probability about . (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.) P( > 23) (d) Calculate the probability that we will obtain a sample mean less than 20.487; that is, calculate P( < 20.487) (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.) P( < 20.487)

Homework Answers

Answer #1

Solution :

Given that ,

= 21

= / n = 8 / 79 = 0.9

c) P( > 23) = 1 - P( < 23)

= 1 - P[( - ) / < (23 - 21) / 0.9 ]

= 1 - P(z < 2.22)   

= 1 - 0.9868

= 0.0132

d) P( < 20.487) = P(( - ) / < (20.487 - 21) / 0.9)

= P(z < -0.57)

Using z table

= 0.2843

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that we will randomly select a sample of n = 88 elements from a population...
Suppose that we will randomly select a sample of n = 88 elements from a population and that we will compute the sample proportion of these elements that fall into a category of interest. If the true population proportion p equals .9: (a) Describe the shape of the sampling distribution of . Why can we validly describe the shape? (b) Find the mean and the standard deviation of the sampling distribution of . (Round the answers to 2 decimal places.)
Suppose that we will randomly select a sample of n = 117 elements from a population...
Suppose that we will randomly select a sample of n = 117 elements from a population and that we will compute the sample proportion   of these elements that fall into a category of interest. If the true population proportion p equals .7: (a) Describe the shape of the sampling distribution of . Why can we validly describe the shape? (b) Find the mean and the standard deviation of the sampling distribution of . (Round the answers to 2 decimal places.)
Suppose that we will take a random sample of size n from a population having mean...
Suppose that we will take a random sample of size n from a population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean  : (a) µ = 20, σ = 2, n = 41 (Round your answers of "σ" and "σ2" to 4 decimal places.) µ σ2 σ (b) µ = 502, σ = .7, n = 132 (Round your answers of...
Suppose that we will take a random sample of size n from a population having mean...
Suppose that we will take a random sample of size n from a population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean : (a) µ = 18, σ = 2, n = 22 (Round your answers of "σ " and "σ 2" to 4 decimal places.) (b) µ = 494, σ = .3, n = 125 (Round your answers of...
A random sample of size n = 50 is selected from a binomial distribution with population...
A random sample of size n = 50 is selected from a binomial distribution with population proportion p = 0.8. Describe the approximate shape of the sampling distribution of p̂. Calculate the mean and standard deviation (or standard error) of the sampling distribution of p̂. (Round your standard deviation to four decimal places.) mean = standard deviation = Find the probability that the sample proportion p̂ is less than 0.9. (Round your answer to four decimal places.)
1. Suppose a random sample of 100 elements is selected from a non-normally distributed population with...
1. Suppose a random sample of 100 elements is selected from a non-normally distributed population with a mean of µ = 30 and a standard deviation of σ = 8. a. What is the expected value of ?̅? b. What is the standard error of the mean ??̅? c. What is the sampling distribution of ?̅? Describe its properties. d. If we select a random sample of size n = 100, what is the probability that ?̅will fall within ±...
A random sample of n = 81 observations is drawn from a population with a mean...
A random sample of n = 81 observations is drawn from a population with a mean equal to 15 and a standard deviation equal to 9 . Complete parts a through g below. a. Give the mean and standard deviation of the? (repeated) sampling distribution x overbar . mu Subscript x overbar equalsnothingsigma Subscript x overbar equalsnothing ?(Type integers or? decimals.) b. Describe the shape of the sampling distribution of x overbar . Does this answer depend on the sample?...
1. A sample of 6 voters to be randomly drawn from the U.S population, when 50%...
1. A sample of 6 voters to be randomly drawn from the U.S population, when 50% vote Republican. a. The number of Republican voters in this sample can vary from 0 to 6. Find its probability distribution. b. Calculate the mean and standard deviation. c. Use the binomial mean and variance formula to verify your results in b. d. What is the probability of exactly 2 Republican voters in the sample? Use the following table to do part a and...
suppose a random sample of n measurements is selected from a binomial population with probability of...
suppose a random sample of n measurements is selected from a binomial population with probability of success p=0.31. given n=300. describe the shape, and find the mean and the standard deviation of the sampling distribution of the sample proportion
Suppose a random sample of n measurements is selected from a binomial population with probability of...
Suppose a random sample of n measurements is selected from a binomial population with probability of success p = .38. Given n = 300, describe the shape, and find the mean and the standard deviation of the sampling distribution of the sample proportion,  .
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT