It's a simple rule: whoever gets home first puts the dogs out. Marsha left to do grocery shopping at 4 PM, and her entire trip (driving plus store shopping) is normally distributed with a mean of 90 minutes and a standard deviation of 20 minutes. John leaves his office promptly at 5:15 PM, and the time it takes him to get home (in minutes) has a discrete distribution given below.

John's Time to Get Home

Probability

9. 0.05

11. 0.05

13. 0.1

15. 0.15

17. 0.25

19. 0.15

21. 0.1

23. 0.05

25. 0.05

27. 0.05

a.Who let the dogs out, John or Marsha? Estimate the probability that Marsha put them out vs the probability that John put them out.

b.What is the expected time (i.e., average time) the dogs went out? (Give your answer in clock time, e.g., "5:52 PM." You may round to the nearest minute.)

c.What is the probability that the dogs went out after 5:45 PM?