Vivian Lowe is planning a surprise party for her husband’s 50th birthday. She has decided to serve shish kabob. The recipe that she is using calls for two pineapple chunks for each shrimp. She plans to size the kabobs so that each has three shrimp. She estimates that a single pineapple will yield about 50 chunks, but from past experience, about 1 out of every 10 pineapples is bad and has to be thrown out. She has invited 200 people and expects that about half will show up. Each person generally eats about 2 kabobs.

a. How many pineapples should she buy?

b. Suppose that the number of guests is a random variable having the normal distribution with mean 100 and variance 1,680. If she wants to make enough kabobs to feed all the guests with probability 95 percent, how many pineapples should she buy?