Question

Question: Star Cat Books, a small independent bookstore in Bradford is trying to decide whether to disconti... Star Cat Books, a small independent bookstore in Bradford is trying to decide whether to discontinue selling magazines. The owner suspects that only 9% of the customers buy a magazine and thinks that she might be able to use the display space to sell something more profitable. Before making a final decision, she decides that for one day she'll keep track of the number of customers and whether or not they buy a magazine. What is the probability that exactly 4 of the first 15 customers buy magazines? What is the probability that at least 10 of his first 50 customers buy magazines? She had 72 customers that day. Assuming this day was typical for his store, what would be the mean and standard deviation of the number of customers who buy magazines each day? Surprised by the high number of customers who purchased magazines that day, the owner decided that her 9% estimate must have been too low. How many magazine sales would it have taken to convince you? Justify your answer. (Please show all of your work and do not use a graphing calculator, thank you!

Answer 1

Let X is a random variable shows the number of customers buy a magazine.

What is the probability that exactly 4 of the first 15 customers buy magazines?

Here X has binomial distribution with parameters n=15 and p=0.09. The probability that exactly 4 of the first 15 customers buy magazines is

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What is the probability that at least 10 of his first 50 customers buy magazines?

Here X has binomial distribution with parameters n=50 and p=0.09. The probability that at least 10 of his first 50 customers buy magazines is

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Now X has binomial distribution with parameters n=72 and p=0.09. The mean is

and standard deviation

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The usual range of values is

So you need to sold at least 12 magazine to convince that 9% estimate must have been too low.