# statistics and probabilities - 68332

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(6.2) Standard Normal Distribution. In the following exercises, assume that the thermometer readings are normally distributed with a mean of 0 degrees celcius and a standard deviation of 1.00 degrees celcius. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celcius degrees.) Round answers to four decimal places.

18- Less than -2.75

22- Greater than 2.33

26- Between 1.00 and 3.00

42- Finding critical values. In this exercise, find the indicated value. z0.01

(6.3) Marine corps height requirement for men. The U.S. marine corps requires that men have heights between 64 and 80 inches. Men's heights are normally distributed with a mean of 69.0 inches with a standard deviation of 2.8 inches.

26- A. Find the percentage of men who meet the height requirement. Are many men denied the opportunity to become a Marine because they do not satisfy the height requirement?

B- If the height requirements are changed so that all men are eligible except the shortest 3% and the tallest 4%, what are the new height requirements?

(6.4) 10- Assume that the samples of size n=2 are randomly selected without replacement from the population consisting of 2,3, and 10, where the values are the numbers of people in households. The following table lists the nine different possible samples.

Sample               Sample Range                  Probability

2.2                     0                                    1/9

2.3                     1                                    1/9

2.10                   8                                     1/9

3.2                     1                                     1/9

3.3                     0                                     1/9

3.10                   7                                      1/9

10.2                   8                                      1/9

10.3                    7                                    1/9

10.10                  0                                     1/9

A-Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviaitions in the format of a table representing the probability distribution. Hint- use a format similar to the table.

B- Compare the population standard deviation to the mean of the sample standard deviations.

C- Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

12-Repeat following exercise using means instead of standard deviations.

(6.5) 12- Effect of diet on length of pregnancy. The lengths of pregnancy are normally distributed with a mean of 268 days and a standard deviation of 15 days.

A- If one pregnant woman is randomly selected, find the probability that her length of pregnancy is less than 260 days.

B- If 25 randomly selected women are put on a special diet just before they become pregnant, find the probability that their lengths of pregnancy have a mean that is less than 260 days, assuming the diet has no effect.

C- If the 25 women do have a mean of less than 260 days, does it appear that the diet has an effect on the length of pregnancy , and should the medical supervisors be concerned?

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