Solutions for the
of Chapter 5
5.2 Testing a coin:
a) With a relatively short run, such as 10 flips of a coin, the cumulative proportion of heads can
fluctuate a lot.
b) We’d have to flip the coin many, many times. In the long run, the cumulative proportion
approaches the actual probability of an outcome.
: No. In the short run, the proportion of a given outcome can fluctuate a lot. Only in
the long run does a given proportion approach the actual probability of an outcome.
5.5 Due for a basket
: False. For the typical pro, successive shots are independent, and what happens in
shots already taken does not affect much, if at all, the chance of making future shots.
5.6 Random digits:
(b) is not correct because in the short run, probabilities of each digit being
generated can fluctuate a lot.
5.11 Unannounced Pop Quiz:
a) The results will be different each time this exercise is conducted.
b) We would expect to get about 50 questions correct simply by guessing.
c) The results will depend on your answer to part a.
d) 42% of the answers were “true.” We would expect this percentage to be 50%. They are not
necessarily identical, because observed percentages of a given outcome can fluctuate in the short
e) There are some groups of answers that appear nonrandom. For example, there are strings of five
“trues” and eight “falses,” But this can happen by random variation. Typically, the longest strings
of trues or falses that students will have will be much shorter than these.
5.14 Random digit
a) The sample space is the set of all possible outcomes; in this case, it is all possible single digits: 0,
1, 2, 3, 4, 5, 6, 7, 8, and 9.
b) The probability for each possible outcome is 0.10 because there are ten possible outcomes, and