For some problems, if possible, sketch a little diagram to clearly see the area under the normal curve.

1. A survey of inmates in state correctional facilities reports the length of sentence in years for each of 32inmates. The mean is 14.0 and standard deviation for these data is 11.0, and the data are normally distributed.

a. What is the z-score corresponding to a sentence length of 28 years? How do you interpret this score?

b. What is the z-score corresponding to a sentence length of 5 years? How do you interpret this score?

c. What is the probability that an inmate would have a sentence length of greater than 19 years?