1. The mean age for licensed physicians in the United States is 51.5 years. A government official randomly selects 700 licensed physicians and computes their mean age to be 50.9 years.

a. Which value is the parameter and which the statistic?

b. Is it unreasonable that the mean of the 700 physicians is different than 51.5? Explain.

c. If you collected a random group of 700 physicians would you expect it to be exactly 50.9 (the same as the first group)? Explain.

2. The distribution for the time a patient of a medical center spends waiting for an appointment is normal with a mean of 35 minutes and a standard deviation of 12 minutes. A random sample of 42 patients will be collected and the sample mean waiting time will be computed.

a. What is the mean of the sample mean?

b. What is the standard deviation of the sample mean?

c. If you wanted the standard deviation of the same mean to be 1.25, how big should your sample be?

3. The blood cholesterol levels of men age 55 to 64 are approximately Normal, with a mean of 224 milligrams per deciliter (mg/dl) and a standard deviation of 39 mg/dl. A physician will randomly select 76 men age 55 to 64 and will compute the sample mean. For each question sketch a graph of the distribution demonstrating the value you are asked to find.

a. What interval contains the sample mean for 99.7% of all samples of size 76?

b. What is the probability that the sample mean is greater than 233 mg/dl?