Stratford University Probability Statistics Questions

1. Solve the problem.

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of and a standard deviation of What is the probability that the mean annual snowfall during 25 randomly picked years will exceed

2. For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122.

3. The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 111.8 inches?

4. The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb?

5. The scores on a certain test are normally distributed with a mean score of 60 and a standard deviation of 5. What is the probability that a sample of 90 students will have a mean score of at least 60.527?

6. A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.

7. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of and a standard deviation of If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September is greater than

8. Assume that women’s heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches.

9. Suppose that replacement times for washing machines are normally distributed with a mean of and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than

10. Human body temperatures are normally distributed with a mean of and a standard deviation of If 19 people are randomly selected, find the probability that their mean body temperature will be less than