Question 1

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? (4 marks)

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

score? (4 marks)

Question 2

The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is

45 months. A consumer protection agency that wants to check this claim took a random sample of

24 such batteries and found that the mean life from this sample is 43.05 months. The lives of all such

batteries have a normal distribution with the population standard deviation of 4.5 months. Test the

hypothesis with the alternative (research) hypothesis that the mean life of these batteries is less

than 45 months, using the critical-value approach and . (12 marks)

Note that for , the critical value of z is -1.96.