Question: A T-shirt company is interested in knowing the average retail price charged for one product sold in stores across the country. The company cannot justify a national census to generate this information. Based on the company information system's list of all retailers who carry the product, a researcher for the company contacts 36 of these retailers and ascertains the retail prices for the product. A population standard deviation is known to be $1.13. The price data (in dollar) is listed in the following table.
a) Use Excel to calculate the sample average retail price.
b) Set up a 90% confidence interval of the population average retail price charged for this T-shirt item.
c) Does the population of retail price have to be normally distributed here? Explain briefly.
d) What is the probability that the mean retail price, in a sample of size 36, is greater than $21? Assume the population average retail price is $21.4.