Question

A soft-drink machine is regulated so that it discharges an average of 6.6 ounces per cup. The amount of drink is normally distributed with a standard deviation equal to 0.5 ounces.

Part 1:  (3 points ) What is the probability that a cup will contain more than 7.54 ounces?

Part 2:  (3 points ) What is the probability that a cup contains between 6.54 and 7.06 ounces?

Part 3: (4 points ) Suppose we want to regulate this machine so that only 5% of the drinks go above a certain value. What should be that cut off value for this soft-drink machine?

Part 4: The machine is checked periodically by taking a sample of 9 drinks and computing the average content. If  falls in the interval , the machine is thought to be operating satisfactorily, otherwise, we conclude that  ounces.

i)   (3 points ) Find the probability of committing a Type I error when  ounces.

ii)  (3 points ) Find the probability of committing a Type II error when  ounces.

Answer 1

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