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# The probability distribution shown here describes a ISBN: 9780321826237 51

## Solution for problem 1E Chapter 5

Statistics for Business and Economics | 12th Edition

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Problem 1E

Problem 1E

The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency:

 x 0 2 4 6 p(x) ¼ ¼ ¼ 1/4

a. List all the different samples of n = 2 measurements that can be selected from this population.

b. Calculate the mean of each different sample listed in part a.

c. If a sample of n = 2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?

d. Assume that a random sample of n = 2 measurements is selected from the population. List the different values of x̄found in part b and find the probability of each. Then give the sampling distribution of the sample mean x̄ in tabular form.

e. Construct a probability histogram for the sampling distribution of x̄.

Step-by-Step Solution:

Step 1 of 6:

Given the probability distribution describes a population of measurements that can assume values of 0, 2, 4 and 6 each of which occurs with the same relative frequency.

 x 0 2 4 6 p(x)    Step 2 of 6:

a). To list all the different samples of n = 2 measurements that can be selected from this population.

The different samples of n = 2 with replacement and their means are:

 Possible samples (0,0) (0,2) (0,4) (0,6) (2,0) (2,2) (2,4) (2,6) (4,0) (4,2) (4,4) (4,6) (6,0) (6,2) (6,4) (6,6)

Step 3 of 6:

b). To calculate the mean of each different sample listed in part(a).

 Possible samples Mean ( (0,0) 0 (0,2) 1 (0,4) 2 (0,6) 3 (2,0) 1 (2,2) 2 (2,4) 3 (2,6) 4 (4,0) 2 (4,2) 3 (4,4) 4 (4,6) 5 (6,0) 3 (6,2) 4 (6,4) 5 (6,6) 6

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321826237

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