# Question

A manufacturer of stone-ground, deli-style mustard uses a high-speed machine to fill jars.The amount of mustard dispensed into the jars forms a normal distribution with a mean 290 grams and a standard deviation 4 grams. Each hour a random sample of 12 jars is taken from that hour’s production. If the sample mean is between 287.74 and 292.26, that hour’s production is accepted; otherwise, it is rejected and the machine is recalibrated before continuing.

a. What is the probability of the type I error by rejecting the previous hour’s production when the mean jar weight is 290 grams?

b. What is the probability of the type II error by accepting the previous hour’s production when the mean jar weight is actually 288 grams?

a. What is the probability of the type I error by rejecting the previous hour’s production when the mean jar weight is 290 grams?

b. What is the probability of the type II error by accepting the previous hour’s production when the mean jar weight is actually 288 grams?

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