Data analytics
Question # 6, Page 194, Use data P05_06.xlsx
6. A local beer producer sells two types of beer, a regular
brand and a light brand with 30% fewer calories. The
company’s marketing department wants to verify that its
traditional approach of appealing to local white-collar
workers with light beer commercials and appealing to
local blue-collar workers with regular beer commercials
is indeed a good strategy. A randomly selected group
of 400 local workers are questioned about their beer-drinking
preferences, and the data in the file P05_06.
xlsx are obtained.
a. If a blue-collar worker is chosen at random from this
group, what is the probability that he/she prefers light
beer (to regular beer or no beer at all)?
b. If a white-collar worker is chosen at random from this
group, what is the probability that he/she prefers light
beer (to regular beer or no beer at all)?
c. If you restrict your attention to workers who like to
drink beer, what is the probability that a randomly
selected blue-collar worker prefers to drink light beer?
d. If you restrict your attention to workers who like to drink
beer, what is the probability that a randomly selected
white-collar worker prefers to drink light beer?
e. Does the company’s marketing strategy appear to be
appropriate? Explain why or why not.
Question # 11, Page 199, No Data Required
The National Football League playoffs are just about to
begin. Because of their great record in the regular season,
the Steelers get a bye in the first week of the playoffs.
In the second week, they will play the winner of the
game between the Ravens and the Patriots. A football
expert estimates that the Ravens will beat the Patriots
with probability 0.45. This same expert estimates that
if the Steelers play the Ravens, the mean and standard
deviation of the point spread (Steelers points minus
Ravens points) will be 6.5 and 10.5, whereas if the
Steelers play the Patriots, the mean and standard deviation
of the point spread (Steelers points minus Patriots
points) will be 3.5 and 12.5. Find the mean and standard
deviation of the point spread (Steelers points minus their
opponent’s points) in the Steelers game.
Question # 24, Page 214, No Data Required
24. It is widely known that many drivers on interstate highways
in the United States do not observe the posted speed limit.
Assume that the actual rates of speed driven by U.S. motorists
are normally distributed with mean m mph and standard
deviation 5 mph. Given this information, answer each of the
following independent questions. (Hint: Use Goal Seek in
parts a and b, and use the Solver add-in with no objective in
part c. Solver is usually used to optimize, but it can also be
used to solve equations with multiple unknowns.)
a. If 40% of all U.S. drivers are observed traveling at 65
mph or more, what is the mean m?
b. If 25% of all U.S. drivers are observed traveling at 50
mph or less, what is the mean m?
c. Suppose now that the mean m and standard deviation
s of this distribution are both unknown. Furthermore,
it is observed that 40% of all U.S. drivers travel
at less than 55 mph and 10% of all U.S. drivers travel
at more than 70 mph. What must m and s be?
Question # 42, Page 226, No Data Required
Suppose you are sampling from a large population,
and you ask the respondents whether they believe men
should be allowed to take paid paternity leave from their
jobs when they have a new child. Each person you sample
is equally likely to be male or female. The population
proportion of females who believe males should be
granted paid paternity leave is 56%, and the population
proportion of males who favor it is 48%. If you sample
200 people and count the number who believe males
should be granted paternity leave, is this number binomially
distributed? Explain why or why not. Would your
answer change if you knew your sample was going to
consist of exactly 100 males and 100 females?
Question # 46, Page 230, No Data Required
46. Suppose that the times between arrivals at a bank during
the peak period of the day are exponentially distributed
with a mean of 45 seconds. If you just observed
an arrival, what is the probability that you will need
to wait for more than a minute before observing the
next arrival? What is the probability you will need to