1) A variable of a population has a mean of =200 and a standard deviation of =35.

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean _BLANK _and standard deviation _BLANK_ .

2)The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean =539.6 and standard deviation =28.7.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 545 or higher? ANSWER: For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x, of 25 students? The mean of the sampling distribution for x is: ANSWER The standard deviation of the sampling distribution for x is: ANSWER

(c) What z-score corresponds to the mean score x of 545? ANSWER:

(d) What is the probability that the mean score x of these students is 545 or higher? ANSWER:

3)A company sells sunscreen in 500 milliliter (ml) tubes. In fact, the amount of lotion in a tube varies according to a normal distribution with mean =497 ml and standard deviation =6 ml. Suppose a store which sells this sunscreen advertises a sale for 6 tubes for the price of 5. Consider the average amount of lotion from a random sample of 6 tubes of sunscreen and find:

(a) The standard deviation of the average, x : ANSWER

(b) The probability that the average amount of sunscreen from 6 tubes will be less than 489 ml. Answer:

4) Shelia'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 129 mg/dl and standard deviation 10mg/dl. Let L denote a patient's glucose level.

(a) If measurements are made on four different days, determine L such that there is a probability of only 0.03that the mean glucose level of four test results falls above L for Shelia's glucose level distribution. What is the value of L? In other words, determine the value of L so that P(x>L)=0.03. Answer:

(b) If measurements are made on four different days, and the mean result from the four tests is compared to the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes? Answer: