A store surveys customers to see if they are satisfied with the service they received. Samples of 25 surveys are taken.One in five people are unsatisfied. What is the variance of the mean of the sampling distribution of sample proportions forthe number of unsatisfied customers? What is the variance for satisfied customers?

Question
Asked Oct 22, 2019
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A store surveys customers to see if they are satisfied with the service they received. Samples of 25 surveys are taken.
One in five people are unsatisfied. What is the variance of the mean of the sampling distribution of sample proportions for
the number of unsatisfied customers? What is the variance for satisfied customers?

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Expert Answer

Step 1

Form the given information,

Population proportions;

p = 1/5.

q = 1- p = 4/5.

Sample size(n) =25.

Step 2

Let X be number of unsatisfied customers in the sample.

X follow the binomial distribution with p =1/5 and n =25.

Thus,

E(X) ng
1
= 25x
= 5
V (X)= npq
4
1
= 25x=x.
5 5
=4
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E(X) ng 1 = 25x = 5 V (X)= npq 4 1 = 25x=x. 5 5 =4

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