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 1.54.
b. For a randomly selected subject, find the probability of a bone density test score greater than -1.54.
c. For a randomly selected subject, find the probability of a bone density test score between -1.33 and 2.33.
d. Find Q1, the bone density test score separating the bottom 25% from the top 75%.
e. If the mean bone density test score is found for 9 randomly selected subjects, find the probability that the mean is greater than 0.50.