Circuit Citys receipts show that customer purchase amounts have a right-skewed d

Question

Circuit Citys receipts show that customer purchase amounts have a right-skewed distribution with a mean of $49 and a standard deviation of $21. Suppose the Circuit City store in Syracuse had 502 customers yesterday. Describe the sampling distribution of the stores total revenues. In the specific, answer the following questions: (i) Is the distribution Normal? If so, why? (ii) What is the mean of this distribution? What is the standard deviation of this distribution? Estimate the probability that the stores revenues were at least $20,000. If in a typical day the store serves 502 customers, how much does the store take in on the worst 5% of such days?

Explanation / Answer

samplinf distribution of stores total revenue is normal due to large sample size.

mean of the distribution =49*502 =24598

and std deviation =21*(502)1/2 =470.5125

2)hence P(X>20000)=1-P(Z<(20000-24598)/470.5125)=1-P(Z<-9.7772)=1-0 ~1

3) for worst 5% ; z=-1.645

hence corrresponding value =24598-1.645*470.5125=23824.08

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