A bone mineral density test is used to identify a bone disease. The result of a bone density test is commonly measured as a z score, and the population of z scores is normally distributed with a mean of 0 and a standard deviation of 1.
a. For a randomly selected subject, find the probability of a bone density test score less than 2.93.
b. For a randomly selected subject, find the probability of a bone density test score greater than -1.53.
c. For a randomly selected subject, find the probability of a bone density test score between
-1.07 and 2.07.
d. Find P30, the bone density test score separating the bottom 30% from the top 70%.
e. If the mean bone density test score is found for 16 randomly selected subjects, find the probability that the mean is greater than 0.27.