Prison Sentences. Researchers M. Dhami et al. discussed how people adjust to prison life in the article "Adaption to Imprisonment" (Criminal Justice and Behavior, Vol. 34, No. 8, pp. 1085-1100). A sample of 712 federally sentenced adult male prisoners had an average sentence of 9.15 years. Assume that, for federally sentenced adult male prisoners, the population standard deviation of sentence length is 17.2 years.

a. Find and interpret a 90% confidence interval for the mean sentence length, , of all federally sentenced adult male prisoners.

b. Under what conditions can you freely apply the procedure that you used in part (a)?