a) A random variable X has an exponential distribution with mean = . Find: i. P(X > 3) ii. P(X > 2) iii. P(X > 3| X > 2) iv. Show that P(X> 1) = P(X > 3| X > 2)

b) Does an average box of cereal contain 368 grams of cereal as claimed by a company? A random sample of 25 of these boxes of cereal showed X = 372.5. The company has specified to be 15 grams. Test this claim at = 0.05 significance level.