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 210 milliliters and a standard deviation of 12 milliliters. The machine is checked periodically by taking a sample of 16 drinks and computing the average content. If x falls in the interval 201

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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 210 milliliters and a standard deviation of 12
milliliters. The machine is checked periodically by taking a sample of 16 drinks and computing
the average content. If x falls in the interval 201 <x<219, the machine is thought to be operating
satisfactorily; otherwise, the owner concludes that µ +210 milliliters. 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 committing a type I error when u =210 milliliters.
The probability is 0.0026 .
(Round to four decimal places as needed.)
(b) Find the probability of committing a type Il error when u = 222 milliliters.
The probability is
(Round to four decimal places as needed.)
Transcribed Image Text: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 210 milliliters and a standard deviation of 12 milliliters. The machine is checked periodically by taking a sample of 16 drinks and computing the average content. If x falls in the interval 201 <x<219, the machine is thought to be operating satisfactorily; otherwise, the owner concludes that µ +210 milliliters. 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 committing a type I error when u =210 milliliters. The probability is 0.0026 . (Round to four decimal places as needed.) (b) Find the probability of committing a type Il error when u = 222 milliliters. The probability is (Round to four decimal places as needed.)
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