Question

Suppose that in a particular state, female offenders sentenced to prison received a mean sentence length of 30 months (s=12) and male offenders' mean sentence length was 40 months (s=10). If you randomly selected a female prison inmate and found that she had been sentenced to 24 months, would you be surprised? What about if she was serving a 45-month sentence? If you randomly selected a male inmate who had a 60 month-sentence, would you be surprised to find this result? What about if this sentence was 31 months? Explain your answers

Answer 1

The plus-minus one standard deviation of the female is (30-12, 30+12)= (18, 42). The 24 months sentenced of the female fall in this interval. Hence, we would not be surprised. Whereas, the 45 months sentence of the female is falling within the plus-minus two standard deviations ((30-2*12, 30+2*12)=(6, 54). Hence, this 45 months sentence also not surprised whereas it is more surprised than 24 months sentence.

Similarly, the plus-minus two standard deviations of the male are (40-2*10, 40+2*10)= (20, 60). The 60 months sentenced of the male fall in this interval. Hence, we would not be surprised. Whereas, the 31 months sentence of the male is falling within the plus-minus one standard deviation ((40-10, 40+10)=(30, 50). Hence, this 31 months sentence also not surprised whereas it is less surprised than 60 months sentence.