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

wait at least two minutes?