Completeness of your results and explanations. 11) Mail carriers at a certain post office can earn bonus pay based on the number of houses they are able to deliver mail to in one day. To determine whether a particular mail carrier earns a bonus, one day is selected at random and the number of houses the mail carrier is able to deliver mail to
that day is counted and used to determine that mail carrier's bonus at the end of the year. The
daily number of houses this mail carrier delivers mail to is approximately normally distributed
with mean of 120 houses and standard deviation of 10.5 houses. a.) If the mail carrier is able to deliver to more than 140 houses on the day the number of
deliveries is counted, the mail carrier gets a bonus at the end of the year. Approximately
what is the probability that this mail carrier will receive a bonus? (Assume that the mail
carrier does not know that the number of houses she delivers mail to is being counted).

b.) The mail carriers' union suggests that instead of choosing one day at random, the post
office should choose 3 days at random. With the suggested plan, the mail carrier would
only receive a bonus at the end of the year if the mean number of houses she delivers
mail to for the 3 days is greater than 140. Would the mail carrier be more likely, less
likely, or equally likely to receive a bonus using the suggested plan compared to the
plan described in part (a)? Justify your choice.

c.) A typical work week consists of the days Monday, Tuesday, Wednesday, Thursday, and
Friday. The post office manager believes that the number of houses the mail carrier is
able to deliver mail to tends to be greater on Mondays and Fridays, and there is concern
that the mail carrier will unfairly earn her bonus if the delivery count occurs on a
Monday or Friday. If one work day is chosen at random from each of 3 typical work
weeks, what is the probabilty that none of the 3 days