Several drugs are used to treat high blood pressure. A sales specialist for a leading pharmaceutical company randomly sampled the records of 10 sales districts to estimate the number of new prescriptions that had been written during a particular month for the company’s new blood pressure medication. The numbers of new prescriptions were as follows:

210, 240, 190, 275, 290, 265, 312, 284, 261, 243

a. Find a 90% confidence interval for the average number of new prescriptions written for this new drug among all the sales districts. What are the assumptions?

b. Assuming that the confidence level remains constant, what sample size is needed to reduce by half the margin of error of the confidence interval in part a?