7.3 Exercise 11

A study was done about a medical condition that affects a certain group of people. The age range of the people was 14–61. The mean age was 30.9 years with a standard deviation of nine years.

1. In a sample of 25 people, what is the probability that the mean age of the people is less than 35?
2. Is it likely that the mean age of the sample group could be more than 50 years? Interpret the results.
3. In a sample of 49 people, what is the probability that the sum of the ages is no less than 1,600?
4. Is it likely that the sum of the ages of the 49 people are at most 1,595? Interpret the results.
5. Find the 95^th percentile for the sample mean age of 65 people. Interpret the results.
6. Find the 90^th percentile for the sum of the ages of 65 people. Interpret the results.