Testing:the central limit theorem

1. Diastolic blood pressures are assumed to follow a normal distribution with a mean of 85 and a standard deviation of 12.

a. What proportion of people have diastolic blood pressure less than 90?
b. What proportion have diastolic blood pressures between 80 and 90?
c. If someone has a diastolic blood pressure of 100, what percentile is he/she in?

2. Total cholesterol in children aged 10-15 is assumed to follow a normal distribution with a mean of 191 and a standard deviation of 22.4.

a. What proportion of children 10-15 years of age have total cholesterol between 180 and 190?
b. What proportion of children 10-15 years of age would be classified as hyperlipidemic (Assume that hyperlipidemia is defined as a total cholesterol level over 200)?
c. If a sample of 20 children are selected, what is the probability that the mean cholesterol level in the sample will exceed 200?


3. Among coffee drinkers, men drink a mean of 3.2 cups per day with a standard deviation of 0.8 cups. Assume the number of drinking per day follows a normal distribution.

a. What proportion drink 2 cups per day or more?
b. What proportion drink no more than 4 cups per day?
c. If the top 5% of coffee drinkers are considered heavy coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker?
d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?