(Solved): part b A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is a ...

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 mililiters and a standard deviation of 10 mililiters. The machine is checked periodically by taking a sample of 4 drinks and computing the average content. If \( x \) falls in the interval \( 193<\bar{x}<207 \), the machine is thought to be operating satisfactorily, otherwise, the owner concludes that \( \mu \neq 200 \) milliiters, Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Find the probability of commiting a type I error when \( \mu=200 \) milliliters. The probability is \( 0.1615 \), (Round to four decimal places as needed.) (b) Find the probability of committing a type \( \| \) error when \( \mu=190 \) milliliters. The probability is (Round to four decimal places as needed.)