Question: A company that sells its products through mail order catalogs wants information about the success of its most recent catalog. The company decides to estimate the mean dollar amount of the items ordered from those who received the catalog. For a random sample of 100 customers from their files, only 5 made an order so 95 of the response values were 0$. The overall mean of all 100 orders was $10, with a standard deviation of $10.

a. Is it plausible that the population distribution is normal? Explain and discuss how much this affects the validity of a confidence interval of the mean.

b. Find a 95% confidence interval for the mean dollar order for the population of all customers who received this catalog. Normally, the mean of their sales per catalog is about $15. Can we conclude that it declined with this catalog.