Paraphrased problems from EMBS
42. (p 191) In the past, 5% of cardholders of a local bank defaulted. Hence, management thought a
randomly selected cardholder would default with probability 0.05. The bank also found the probability
of missing a monthly payment to be 0.20 for cardholders who did not go on to default and 1.00 for
cardholders who do default. A cardholder has missed a monthly payment. What it the probability that
cardholder will default?
36. (p 225). According to a survey involving a VERY large number of people, TD Amertrade found that
one in four have exchange-traded funds in their portfolios (USA Today, Jan 11, 2007). For a random
sample of 20 investors….
a. Compute the probability that exactly 4 investors have exchange-traded funds in their portfolios.
b. Compute the probability that at least 2 investors have exchange-traded funds in their portfolios.
c. If you found that 12 of the 20 had exchange-traded funds in their portfolios, would you doubt
the accuracy of the survey results?
d. What is the expected number of investors of the 20 who will have exchange-traded funds in
their portfolios?
e. What is the variance of the number of investors who will have exchange-traded funds in their
portfolios?
18. (p 260). The average stock price for companies making up the S&P 500 is $30 with a standard
deviation of $8.2 (Business Week, Spring 2003). Assumes the stock prices are normally distributed.
a. What is the probability a randomly chosen company will have a stock price of at least $40?
b. What is the probability a randomly chosen company will have a stock price no higher than $20
c. How high must the stock price be to put the company in the top 10%?
14. (p 472). The traditional distribution of colors for plain M&Ms was reported by the firm to be
Brown
Yellow
Red
Orange
Green
Blue
30%
20%
20%
10%
10%
10%
To check these claims, a random sample of 506 plain M&Ms was collected and counted with the
following result:
Brown
Yellow
Red
Orange
Green
Blue
177
135
79
41
36
38
Use α = 0.05 (what else?) to test whether the data support the probabilities reported by the company.
18 (p 474). A very large study reported that airline customers rate their satisfaction with airlines with
the following probabilities: Excellent (3%), Good (28%), Fair (45%) and Poor (24%) (Business Week,
2000). A random sample of 400 adults rating their satisfaction with telephone companies found 24
excellent, 124 good, 172 fair, and 80 poor ratings. Use α = 0.01 to test whether the telephone ratings
could have come from the ratings probabilities associated with the airlines.
Answer from the back of EMBS
42. P(Default given Missed) = 0.05/0.24 = 0.21
The 0.24 was calculated as 0.05(1) + 0.95(0.2)
36 a. 0.189, b. 0.9757, c. yes because it is a very rare event. P(12 or more) = 1-binomdist(11,20,.25,true),
d. n*p = 20*.25= 5, e. n*p*(1-p) = 20*.25*.75 = 3.75.
18.
a. 1-normdist(40,30,8.2,true) = 1-0.888 = 0.1112
b. normdist(20,30,8.2) = 0.1112 (the same as above because of symmetry)
c. norminv(.9,30,8.2) = $40.5.
14. calculated chi-squared = 29.51. P-value = chidist(29.51,5) = 1.83809E-05. Reject H0
18. calculated chi-squared = 16.31. P-value = chidist(16.31,3) = 0.00098. Reject H0.