Other Problems

1. The National Health and Nutritional Examination Survey (NHANES) of 1988-1994 estimated the mean serum cholesterol level for U.S. females aged 20-74 to be 204 mg/dl. The estimate of the standard deviation was approximately 44 mg/dl. Using these estimates as the mean and standard deviation of the entire population of U.S. females, consider the sampling distribution of the sample mean based samples of 50 drawn from women in this age group.

a. What is the mean of the sampling distribution of sample means

b. What is the standard error?

c. Construct an interval that should contain 99% of the sample means.

2. The same study from question 1 focused on women aged 20-29 years. The mean cholesterol level for the entire population in that age group was 183 mg/dl. The standard deviation of that entire population is 37 mg/dl. If a sample of 60 is drawn from this population, find the probability that a sample mean serum cholesterol level is:

a. Between 170 mg/dl and 195 mg/dl

b. Below 175 mg/dl

c. Greater than 190 mg/dl

3. The same study from question 1 focused on women aged 20-29 years. The mean cholesterol level for the entire population in that age group was 183 mg/dl. The standard deviation of that entire population is 37 mg/dl. If a sample of 60 is drawn from this population, find the probability that an individual in this population's serum cholesterol level is:

a. Between 170 mg/dl and 195 mg/dl

b. Below 175 mg/dl

c. Greater than 190 mg/dl