What's Normal? Before you answer this question, please read all of Section 14.5 of the textbook. It contains ideas as well as code that will be useful. In any part of this question that involves a sample size, you can assume the sample size is big enough for the Central Limit Theorem approximation to be good. But pay attention to what is being approximated by the CLT.

a) A simple random sample of 1000 faculty members was taken among all universities in a country. For each sampled faculty member, the surveyors noted the number of papers published in the past year. These 1000 counts had a mean of 1.1 and an SD of 1.8. Does the Central Limit Theorem say that the distribution of the counts is roughly normal? If not, what do you think is the shape of that distribution? Explain based on the information given in the problem.
b) Continuing Part a, construct an approximate 90% confidence interval for the mean number of papers published by faculty at all universities in the country in the past year. Justify your answer. If it is not possible to construct the interval, explain why not.