Probability: Sampling Distribution

1. Scores for men on the verbal portion of the SAT test are normally distributed with a mean of 509 and a standard deviation of 112. Randomly selected men are given the Columbia Review Course before taking the SAT test. Assume that the course has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 590.

2. The heights (in inches) of the five starting basketball players for the Houston Rockets are 85, 79, 82, 73 and 78. Assume that samples of size 2 are randomly selected with replacement from the above population of five heights. Find the mean of the sampling distribution.

3. Here are the numbers of sales per day that were made by Kim Ryan, a courteous telemarketer who worked four days before being fired: 1, 11, 9 and 3. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Find the mean of the sampling distribution.

4. Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(0 < z < a) = 0.3907, find a.

5. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score separating the top 55% from the others.

6. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. One classic use of the normal distribution is inspired by a letter to "Dear Abbey" in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the U.S. Navy. Given this information, find the probability of a pregnancy lasting 308 days or longer.

7. Assume that men's weights are normally distributed with a population mean of 172 pounds and a population standard deviation of 29 pounds. If one man is randomly selected, find the probability that his weight is between 100 and 165 pounds.

8. Assume that the readings on the thermometers are normally distributed with a mean of 0o and a standard deviation of 1oC . A thermometer is randomly selected and tested. Find the probability of a reading that is between -1.18 and 2.15.

9. Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > d) = 0.9922, find d.

10. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find P80 which is the IQ score separating the bottom 80% from the top 20%.