1. A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. Based on a preliminary study, he guesses that the standard deviation of the population of weight loss is about 10 pounds. How large a sample should he take to estimate the mean weight loss to within 2 pounds, with 99% confidence?Sample Size =2. Suppose that A and B are two events for which P(A)=0.34, P(B)=0.63, and P(B|A)=0.45 Find each of the following:A. P(AandB)=B. P(AorB)=C. P(A|B)=3. Compliments about a waiter’s work occur at a rate of 5 per day, and the number has a Poisson distribution.A. Find the probability that the waiter receives 3 or more compliments in a day.Probability =B. Find the probability that the waiter receives 17 or more compliments in a 4-day period.Probability =4.The time it takes for a runner to run one mile is normally distributed with a mean of 5 minutes and a standard deviation of 1.9 minutes. If a sample of 57 one-mile runs are selected at random, what is the probability that the average time exceeds 5 minutes?Probability =5. Suppose that Z is a value drawn from the standard Normal distribution.A. For what number a will 48% values of Z satisfy Z
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