STAT 008 | Exam II Practice Test Page 78

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EXAM II PRACTICE TEST

1) According to the American Cancer Society’s Cancer Facts & Figures, 2013-2014, “a woman living
in the U.S. has a 12.3% lifetime risk of being diagnosed with breast cancer.” Suppose a random
sample of 60 women in the U.S. is studied. Let X represent the number who will be diagnosed with
breast cancer.

a) Find the mean and standard deviation for the number of women who will be diagnosed with
breast cancer.






b) What is the probability that less than 3 of the 60 women will be diagnosed with breast cancer?












2) Due to price changes, the U.S. Postal Service (USPS) sells a variety of stamps which are used to
supplement stamps from prior to the price change. For example, the recent increase in the cost of
Forever stamps from 46¢ to 49¢ requires the 46¢ stamp to be paired with a 3¢ stamp for mailing. Let
X be the value of these supplemental stamps (in cents). Assume the demand for these stamps follows
the distribution below:

X 1 2 3 4 5 10 20
 P X x 0.05 0.16 0.37 0.12 0.09 0.14 0.07

Calculate the standard deviation for the value of these stamps.









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3) The Census Bureau reports that 50.8% of the U.S. population is female. The Centers for Disease
Control & Prevention (CDC) indicates that 18.1% of the U.S. population smokes cigarettes.
Furthermore, the CDC states that given a person is female, there is a 15.8% chance that she smokes
cigarettes. Consider a randomly selected person from the U.S.. The following events are defined:
F: a person is female
S: a person smokes cigarettes

a) Show that the probability of this person being female and a smoker is 8%, i.e.,
  0.08P F S  .







b) What is the probability that the selected person is a female or a smoker?







c) What is the probability that the selected person is a female but not a smoker?







d) If the selected person is a smoker, what is the probability that the person is female?







e) Are being a female and being a smoker independent events? Support your answer
appropriately.






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4) An entry-level accountant is expected to work long hours during the accounting firm’s “busy
season”. Let X be the number of hours per day an entry level accountant works. X can be described
by a normal distribution with mean 12.9 hours and standard deviation 2.4 hours.

a) Find the mean and standard deviation for the sampling distribution of an entry-level accountant’s
average daily hours for the month of January (31 days).







b) What is the probability that the entry-level accountant’s average number of hours worked per day
for the month of January is between 12 and 14?










c) What is the probability that the entry-level accountant worked more than 15 hours on any given
day in January?










d) How many hours does an entry-level accountant work during the longest 15% of days?