2. Suppose that two teams, A and B, play each other five times over a season (not best of five series, but they play all five games). If Team A has a .6 probability of winning any given game complete the probability distribution below:

(2 points)

XA P(XA)

0 .01

1 .08

2

3

4 5 Total 1.0

a. (3 points) What is the probability that Team A sweeps the season series (wins all five matchups)?

b. (2 points) What is the probability that Team A wins at least three games? c. (1 point) What is the probability that Team A gets swept (does not win a game)?

3. Suppose probation officer caseloads have a mean of 120 offenders and a standard deviation of 10. Assuming caseload sizes are normally distributed, determine

a. (2 points) the probability that a particular probation officer has a caseload between 90 and105 b. (1 point) the probability that a particular probation officer has a caseload larger than 132

c. (1 point) the probability that four (4) probation officers have a caseload larger than 132. Take a second to think about this one

d. (1 point) the percentage of probation officers that have a caseload less than 98? e. (1 point) explain any similarities/differences between your answer for (b) and (d).

4. Suppose that the average number of billable hours for attorneys in large firms is 37.5 with a standard deviation of 4.5, and the average for attorneys in small firms is 31 with a standard deviation of 7.5.

a. (1 point) What is the probability that an attorney in a large firm bills over 40 hours a week? b. (1 point) What is the probability that an attorney in a small firm bills over 40 hours a week? c. (1 point) Explain any similarities and differences between your answers for (a) and (b).