1. [4] (Parts (a) and (b) are separate)

1. Part (a) Mark Wilson has to complete 100 independent tasks every month at his work. The time he takes to complete any single task is modeled by an exponential random variable with mean value of 2 hours. If he completes all of his 100 tasks within 160 hours, he receives a Bonus from the company. Find the probability that Mark receives the Bonus in any given month.

1. Part In a manufacturing company, an experiment is designed to estimate the probability of a defective product with an accuracy 0.01by maintain a confidence coefficient of 0.99. Find the minimum number of products needed in the experiment.