As a sales analyst for the shoe retailer Foot Locker, one of your responsibilities is measuring store productivity and then reporting your conclusion back to management. Foot Locker uses sales per square foot as a measure of store productivity. While preparing your report for the second quarter results (Q2), you are able to determine that annual sales for last year ran at a rate of $406 per square foot. Therefore, $406 per square foot will be your sales estimate for the population of all Foot Locker stores during Q2. For your Q2 Sales Report, you decide to take a random sample of 64 stores. Using annual data from last year, you are able to determine that the standard deviation for sales per square foot for all 3,400 stores was $80. Therefore $80 per square foot will be your population standard deviation when compiling your Q2 report. Management has asked for the probability that your sample mean based on 64 stores is 1) within $15 and 2) within $5 of the population mean and they would 3) like the difference between those probabilities with explanation and a corresponding graphic to illustrate the difference. The graphic will, in general, resemble the image below. It is up to you to calculate the probabilities which span ±$5 and ±$15. What is the probability for ±$5, ±$15, and their difference respectively?
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As a sales analyst for the shoe retailer Foot Locker, one of your responsibilities is measuring store productivity and then reporting your conclusion back to management. Foot Locker uses sales per square foot as a measure of store productivity. While preparing your report for the second quarter results (Q2), you are able to determine that annual sales for last year ran at a rate of $406 per square foot. Therefore, $406 per square foot will be your sales estimate for the population of all Foot Locker stores during Q2. For your Q2 Sales Report, you decide to take a random sample of 64 stores. Using annual data from last year, you are able to determine that the standard deviation for sales per square foot for all 3,400 stores was $80. Therefore $80 per square foot will be your population standard deviation when compiling your Q2 report. |
Management has asked for the probability that your sample mean based on 64 stores is 1) within $15 and 2) within $5 of the population mean and they would 3) like the difference between those probabilities with explanation and a corresponding graphic to illustrate the difference.
The graphic will, in general, resemble the image below. It is up to you to calculate the probabilities which span ±$5 and ±$15.
What is the probability for ±$5, ±$15, and their difference respectively?
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