Case Problems Ch.4
4.3 Financial fraud. In December 2006, the Experian-Gallup Personal Credit Index
survey found that 17% of fraud victims knew the perpetrator as a friend or
acquaintance. Financial fraud includes crimes like unauthorized credit card charges,
withdrawal of money from a savings or checking account, and opening an account in
someone else’s name. Because 17% is approximately 1-in-6, a single fair die can be
used to study the probability that a fraud victim knew the perpetrator. Each roll of the die
will represent the random selection of a single fraud victim. If the die lands with the
number 6 facing up, record this as a fraud victim who knew the perpetrator. If the die
lands with a 1, 2, 3, 4, or 5 facing up, record this as a fraud victim who did not know the
perpetrator.
(a) Roll the die 6 times. How many of these 6 simulated fraud victims knew their
perpetrators? If your 6 rolls did not result in exactly 1 fraud victim who knew the
perpetrator, do you have reason to doubt the fairness of the die?
(b) Roll the die a total of 30 times. How many of these 30 simulated fraud victims knew their
perpetrators?
(c) If possible, combine your 30 rolls with the rolls of fellow students. How many fraud
victims are represented by the combined rolls? How many knew their perpetrators?
Compare the percent who knew their perpetrators in your combined rolls with 1-in-6
(16.67%).
4.18 Moving up. An economist studying economic class mobility finds that the
probability that the son of a lower-class father remains in the lower class is 0.46. What
is the probability that the son moves to one of the higher classes?
4.27 NAEP math scores. Scores on the National Assessment of Educational Progress
12th-grade mathematics test for the year 2000 were approximately Normal with mean
300 points (out of 500 possible) and standard deviation 35 points. Let Y stand for the
score of a randomly chosen student. Express each of the following events in terms of Y
and use the 68–95–99.7 rule to give the approximate probability.
(a) The student has a score above 300.
(b) The student’s score is above 370.
4.51 Normal probabilities. Example 4.11 gives the Normal distribution N(50,000,
5500) for the tread life X of a type of tire (in miles). Calculate the following probabilities:
(a) The probability that a tire lasts more than 50,000 miles.
(b) P(X > 60,000)
(c) P(X ≥ 60,000)