A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 200 milliliters and a standard deviation of 15 milliliters. The machine is checked periodically by taking a sample of 9 drinks and computing the average content. If \overline{x} x
falls in the interval 191<\overline{x}<209,191< x
<209, the machine is thought to be operating satisfactorily; otherwise, we conclude that \mu \neq 200μ

=200 milliliters. (a) Find the probability of committing a type I error when \mu=200μ=200 milliliters. b. Find the probability of committing a type II error when \mu=215μ=215 milliliters.