1. The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.8 ounces and standard deviation 0.12 ounces.
(a) What is the probability that the average weight of a SRS of four of these chocolate bars is between 7.65 and 7.93 ounces?
(b) For a SRS of four of these chocolate bars, what is the level L such that there is a 5% chance that the average weight is less than L?
2. Sally's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 127 mg/dl and standard deviation 8 mg/dl. Let L denote a patient's glucose level.
(a) If measurements are made on three different days, find the level L such that there is probability only 0.01 that the mean glucose level of three test results falls above L for Shelia's glucose level distribution. What is the value of L?
(b) If the mean result from the three tests is compared to the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes?