Question 1. The average annual salary for all U.S. teachers is $29,863. Assume that the distribution is normal and the standard deviation is $5,200.

a. Find the probability that a randomly selected teacher earns at least $35,000 a year.

b. What is the probability that the mean for a sample of 80 teachers' salaries is greater than $30,000?

Question 2. In a study of life expectancy, it was found that the mean age at death in the Philippines was 72 with a standard deviation of 5.8 years. If a sample of 50 Filipino people is selected, find the probability that the mean life expectancy will be,
a. Less than 70 years old.
b. Between 68 and 75 years.

Question 3. The mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume that the variable is normally distributed.
a. If an individual is selected, find the probability that the individual's pressure will be between 118 and 122 mm Hg.
b. If a sample of 35 adults is randomly selected, find the probability that the sample mean will be between 119 and 121 mm Hg.

Question 4. The average breaking strength of a certain steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume that the variable is normally distributed.

Question 5. The standard deviation of a variable is 15. If a sample of 100 individuals are selected compute for

a. The standard error of the mean.

b. What sample size is necessary to double the standard error of the mean?

c. What sample size is needed to cut the standard error of the mean in half?