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Chapter 4: Q127E (page 270)

4.127 Rankings of research universities. Refer to the CollegeChoice2015 Rankings of National Research Universities,Exercise 2.110 (p. 125). Data on academic reputation scores for the top 50 research universities (saved in the file) are listed in the accompanying table. Would you recommend using the normal distribution to approximate the distribution of academic reputation scores?

99 92 94 95 97 91 91 92 92 89 84 85 100 87 83

83 89 79 94 79 79 87 76 67 76 76 76 70 74 64

74 69 66 72 65 76 64 65 61 69 62 69 52 64 64

47 60 57 63 62

Short Answer

Expert verified

The quantile- quantile line and data points are not falling approximately one upon another. So, the normally distributed data score is not recommended.

Step by step solution

01

Given information

Data on academic reputation scores for the top 50 research universities are listed in the accompanying table.

02

Plotting the graph

The above graph shows that the data points do not fall in a straight line.

The maximum data points fall below the quantile-quantile line. The lower portions of the data points above the line and upper portion fall below the line, and only the middle portion of the data points fall on the line.

So, it can be said that the productivity score is not normally distributed, andthe normally distributed data score is entirely not recommended in this case.

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Most popular questions from this chapter

The Apprenticecontestants’ performance ratings. Referto the Significance(April 2015) study of contestants’ performanceson the United Kingdom’s version of the TVshow, The Apprentice, Exercise 2.9 (p. 73). Recall thatthe performance of each of 159 contestants was rated ona 20-point scale. Contestants were also divided into twogroups: those who played for a job and those who playedfor a businesspartnership. These data (simulated, based onstatistics reportedin the article) are saved in the accompanyingfile. Descriptive statistics for each of the two groupsof contestants are displayed in the accompanying Minitabprintout.

a. Determine whether the performance ratings of contestantswho played for a job are approximately normallydistributed.

b. Determine whether the performance ratings of contestantswho played for a business partnership are approximatelynormally distributed.

Descriptive Statistics: Rating

Variable Rating

Price

N

Mean

St.Dev

Minimum

Q

1

median

Q3

Maximum

IQ

R

Job

99

7.879

4.224

1

4

9

11

20

7

Partner

60

8.883

4.809

1

5

8

12

20

7

Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beverage dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount at random anywhere between 6.5and 7.5 ounces inclusive. Suppose has a uniform probability

distribution.

a.Is the amount dispensed by the beverage machine a discreteor a continuous random variable? Explain.

b. Graph the frequency function forX , the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 7 ounces.

c. Find the mean and standard deviation for the distribution graphed in part b, and locate the mean and theinterval μ±2σon the graph.

d. Find P(x≥7).

e. FindP(x<6) .

f. FindP(6.5≤x≤7.25) .

g. What is the probability that each of the next six bottles filled by the new machine will contain more than7.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.

Shear strength of rock fractures. Understanding the characteristics

of rock masses, especially the nature of the fracturesis essential when building dams and power plants.The shear strength of rock fractures was investigated inEngineering Geology(May 12, 2010). The Joint RoughnessCoefficient (JRC) was used to measure shear strength.Civil engineers collected JRC data for over 750 rock fractures.The results (simulated from information provided in the article) are summarized in the accompanying SPSShistogram. Should the engineers use the normal probabilitydistribution to model the behavior of shear strength forrock fractures? Explain

Errors in measuring truck weights. To help highway planners anticipate the need for road repairs and design futureconstruction projects, data are collected on the estimatedvolume and weight of truck traffic on specific roadways (Transportation Planning Handbook, 2016) using specialized “weigh-in-motion” equipment. In an experiment involving repeated weighing of a 27,907-pound truck, it wasfound that the weights recorded by the weigh-in-motionequipment were approximately normally distributed witha mean of 27,315 and a standard deviation of 628 pounds

(Minnesota Department of Transportation). It follows thatthe difference between the actual weight and recordedweight, the error of measurement, is normally distributedwith a mean of 592 pounds and a standard deviation of 628pounds.

a. What is the probability that the weigh-in-motion equipment understates the actual weight of the truck?

b. If a 27,907-pound truck was driven over the weigh-in-motion equipment 100 times, approximately howmany times would the equipment overstate the truck’sweight?

c. What is the probability that the error in the weightrecorded by the weigh-in-motion equipment for a27,907-pound truck exceeds 400 pounds?

d. It is possible to adjust (or calibrate) the weigh-in-motion equipment to control the mean error of measurement. At what level should the mean error beset so the equipment will understate the weight of a27,907-pound truck 50% of the time? Only 40% of thetime

Consider the probability distributions shown here:

  1. Use your intuition to find the mean for each distribution. How did you arrive at your choice?
  2. Which distribution appears to be more variable? Why?
  3. Calculateμ and σ2 for each distribution. Compare these answers with your answers in parts a and b.
See all solutions

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