A bone mineral density test is used to identify bone density. The result is commonly measured as a Z score, which is normally distributed with a mean zero and standard deviation of 1.
a) for a randomly selected subject, find the probability of a bone density test, score less than 0.75

b) for a randomly selected subject, find the probability of a bone density test score between -1.5 and 2.5

c) using 0.05 to identify significant values, use the criteria that a values he is significantly high if P (z or greater) ≤ 0.05 and a value is significantly low if P (z or less) ≤ 0.05. find the bone density test score separating significant values from those that are not significant.

d) using the above criteria, is a bone density test score of 1.95 significant? Explain.