Create an example probability distribution in which the expected value is 15. You must have at least three different values for x.
What are the values for the mean and standard deviation of a standard normal distribution?
What are considered unusual z-score values?
The serum cholesterol levels in milligrams/deciliter (mg/dL) in a certain Mediterranean population are found to be normally distributed with a mean of 160 and a standard deviation of 50. Answer the following:
(a) Determine the z-score for a person from this population that has a cholesterol level of 115. Then find the z-score for someone whose cholesterol level is 242.
(b) If x represents a possible cholesterol level from this population, find P(x > 145).
(c) Find P(100 < x < 200) and give an interpretation of this value.
(d) The top 3% of all people in this group have cholesterol levels that make them "at-risk" for heart problems. Determine the raw-score cholesterol level which separates the at-risk people from the rest of the group.
Does a confidence interval for µ get wider or narrower if:
(a) the percent of desired confidence (confidence level) decreases from 99% to 90%?
(b) the size of the sample used to produce the confidence interval is decreased?
(c) our estimate of the standard deviation gets smaller?