1. In a study of the life expectancy of 500 people in a certain geographic region, the mean age at

death was 72.0 years, and the standard deviation was 5.3 years. If a sample of 50 people from this

region is selected, find the probability that the mean life expectancy will be less than 70 years.

2. A study of 800 homeowners in a certain area showed that the average value of the homes was

$82,000, and the standard deviation was $5000. If 50 homes are for sale, find the probability that

the mean of thevaluesofthesehomesisgreaterthan$83,500.

3. The standard deviation of a variable is 15. If a sample of 100 individuals is selected, compute the

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

4. At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard

deviation is 3.7 years. Assume the variable is normally distributed.

a. If a proofreader from the company is randomly selected, find the probability that his or her age

will be between 36 and 37.5 years.

b. If a random sample of 15 proofreaders is selected, find the probability that the mean age of the

proofreaders in the sample will be between 36 and 37.5 years.