a. Derrick, a biostatistician wants to estimate the average weight loss for people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses is about 4 kilograms. How large a sample should he take to estimate the mean weight loss to within 880 grams, with 90 confidence? b. Many physicians recommend essential blood tests for their patients every year, including complete blood count, liver function tests, and cholesterol level. The following table shows the number of essential blood tests ordered for 80 patients Number of blood tests 0 2 3 4 5 Number of patients 2 11 15 22 29 Construct a 99% confidence interval for the population proportion of patients who have more than 3 essential blood tests