The owner of a pet store is trying to decide whether to discontinue selling spec

Question

The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more profitable items. Before making a final decision, she decides to keep track of the total numberof customers for a day and whether they purchase specialty clothes. In a typical day there are 275 customers. a) Describe the shape of the sampling distribution of the sample proportion. Show the sample size assumption is satisfied for assuming this model. b) What is the mean and standard deviation for the sampling distribution of the sample proportions?

Explanation / Answer

A. Here we will use binomial distribution as probability of success is given =0.04

The sample size assumption is correct as binomial distribution tends to normal with big sample size.

B. Mean =np=275*0.04=11 & variance=np(1-p)=11*0.96=10.56 so sd=sqrt(variance)=3.25

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