A survey of inmates in state correctional facilities reports the length of sentence in years for each of 31 inmates. The mean is 13.38 and standard deviation for these data is 10.15 and the data is normally distributed.

a. What is the z-score corresponding to a sentence length of 30 years? How do you interpret this score?

b. What is the z-score corresponding to a sentence length of 2 years? How do you interpret this score?

c. What is the probability that an inmate would have a sentence length of greater than 15 years?

d. What proportion of inmates would have sentence lengths between 2 years and 15 years?

e. What raw scores fall into the upper 2% of the distribution?