Question: 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

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 x¯ falls in the interval 191 < x <¯ 209, the machine is thought to be operating satisfactorily; otherwise, we conclude that μ = 200 milliliters.

(a) Find the probability of committing a type I error when μ = 200 milliliters.

(b) Find the probability of committing a type II error when μ = 215 milliliters.

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