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Chapter 12: Q. AP4.34 (page 833)

AP4.34 A distribution of exam scores has mean 60and standard deviation 18. If each score is doubled, and then 5is subtracted from that result, what will the mean and standard deviation of the new scores be?

a. mean=115 and standard deviation=31

b. mean=115 and standard deviation=36

c. mean=120 and standard deviation=6

d. mean=120 and standard deviation=31

e. mean=120 and standard deviation=36

Short Answer

Expert verified

The correct answer is option(b) Mean=115 and standard deviation=36.

Step by step solution

01

Given information

To determine the mean and standard deviation of the new scores.

02

Explanation

Given values:
μX=60
σX=18
The mean is determined as follows:
μaX+b=aμX+b
μ2X-5=2μX-5
=2(60)-5
=115

The standard deviation is determined as follows:

σ2X-5=aσX
=2(18)
=36
As a result, the option (b) is the correct option.

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Most popular questions from this chapter

Exercises T12.4–T12.8 refer to the following setting. An old saying in golf is “You drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole (fewer is better) and the player’s total winnings for the previous season are recorded and a least-squares regression line was fitted to the data. Assume the conditions for
inference about the slope are met. Here is computer output from the regression analysis:

T12.6 The P -value for the test in Exercise T12.5 is 0.0087. Which of the following is a correct interpretation of this result?
a. The probability there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b. The probability there is no linear relationship between average number of putts per hole and total winnings for all players on the PGA Tour’s world money list is 0.0087.
c. If there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
d. If there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of −4,139,198 or less is 0.0087.
e. The probability of making a Type I error is 0.0087.

How well do professional golfers putt from various distances to the hole? The scatterplot shows various distances to the hole (in feet) and the per cent of putts made at each distance for a sample of golfers.

The graphs show the results of two different transformations of the data. The first graph plots the natural logarithm of per cent made against distance. The second graph plots the natural logarithm of per cent made against the natural logarithm of distance.

a. Based on the scatterplots, would an exponential model or a power model provide a better description of the relationship between distance and per cent made? Justify your answer.

b. Here is computer output from a linear regression analysis of ln(per cent made) and distance. Give the equation of the least-squares regression line. Be sure to define any variables you use.

c. Use your model from part (b) to predict the per cent made for putts of 21 feet.

d. Here is a residual plot for the linear regression in part (b). Do you expect your prediction in part (c) to be too large, too small, or about right? Justify your answer.

Which of the following is a categorical variable?

a. The weight of an automobile

b. The time required to complete the Olympic marathon

c. The fuel efficiency (in miles per gallon) of a hybrid car

d. The brand of shampoo purchased by shoppers in a grocery store

e. The closing price of a particular stock on the New York Stock Exchange

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

26. Which of the following is the best interpretation of the value 0.4117in the computer output?

a. For each increase of 1cmin foot length, the average height increases by about0.4117cm

b. When using this model to predict height, the predictions will typically be off by about 0.4117cm.

c. The linear relationship between foot length and height accounts for 41.17%of the variation in height.

d. The linear relationship between foot length and height is moderate and positive.

e. In repeated samples of size 25the slope of the sample regression line for predicting height from foot length will typically vary from the population slope by about 0.4117.

Click-through rates Companies work hard to have their website listed at the top of an Internet search. Is there a relationship between a website’s position in the results of an Internet search (1=top position,2=2nd position, etc.) and the percentage of people who click on the link for the website? Here are click-through rates for the top 10 positions in searches on a mobile device:

a. Make an appropriate scatterplot for predicting click-through rate from the position. Describe what you see.

b. Use transformations to linearize the relationship. Does the relationship between click-through rate and position seem to follow an exponential model or a power model? Justify your answer.

c. Perform least-squares regression on the transformed data. Give the equation of your regression line. Define any variables you use.

d. Use your model from part (c) to predict the click-through rate for a website in the 11th position.
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