Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local
paint store in order to paint his mother's house. Unknown to the man, three of these cans
contains an incorrect mix of paint.
For this weekend's big project, the man randomly selects four
of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans
selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find
the probability that none of the four cans selected contains an incorrect mix of paint.
A) 0.25455 B) 0.01818 C) 0.50909 D) 0.21818
Q. 2A sociologist recently conducted a survey of citizens over 60 years of age who have net worths
too high to qualify for Medicaid but have no private health insurance. The ages of the 25
uninsured senior citizens were as follows:
68 73 66 76 86 74 61 89 65 90 69 92 76
62 81 63 68 81 70 73 60 87 75 64 82
Find the upper quartile of the data.
A) 81.5 B) 65.5 C) 92 D) 73
Q. 3As part of a promotion, both you and your roommate are given free cellular phones from a batch
of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the
probability that one of the two phones is faulty.
A) .077 B) .231 C) .538 D) .462
Q. 4At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits
during the tournament. The lower quartile of a particular player's serve speeds was reported to
be 99 mph.
Which of the following interpretations of this information is correct?
A) 75 of the player's serves were hit at speeds greater than 99 mph.
B) 99 serves traveled faster than the lower quartile.
C) 25 of the player's serves were hit at 99 mph.
D) 75 of the player's serves were hit at speeds less than 99 mph.
Q. 5Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All
candidates were told that the positions were randomly filled. Find the probability that two men
are selected to fill the appointed positions.
A) .360 B) .160 C) .343 D) .143
Q. 6Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a
random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in
failed transplants?
A) .296 B) .037 C) .018 D) .333
Q. 7Given that x is a hypergeometric random variable with N = 15, n = 6, and r = 10, compute P(x =
0).
A) .001 B) 0 C) .002 D) 1
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