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Chapter 4: Q124E (page 270)

Ranking PhD programs in economics. Refer to the SouthernEconomic Journal(April 2008) rankings of PhD programsin economics at 129 colleges and universities, Exercise 2.103(p. 117). Recall that the number of publications published byfaculty teaching in the PhD program and the quality of thepublications were used to calculate an overall productivityscore for each program. The mean and standard deviationof these 129 productivity scores were then used to computea z-score for each economics program. The data (z-scores)for all 129 economic programs are saved in the accompanying

file. A Minitab normal probability plot for the z-scores isshown below. Use the graph to assess whether the data areapproximately normal.

Short Answer

Expert verified

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

Step by step solution

01

Given information

The graph of the 129 productivity scores is given,

02

Explanation

From the above graph, it is shown that the data points do not fall in a straight line.

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

So, it can be concluded that the productivity score is not approximately normally distributed.

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Most popular questions from this chapter

Hotels鈥� use of ecolabels. Refer to the Journal of Vacation Marketing (January 2016) study of travelers鈥� familiarity with ecolabels used by hotels, Exercise 2.64 (p. 104). Recall that adult travelers were shown a list of 6 different ecolabels, and asked, 鈥淪uppose the response is measured on a continuous scale from 10 (not familiar at all) to 50 (very familiar).鈥� The mean and standard deviation for the Energy Star ecolabel are 44 and 1.5, respectively. Assume the distribution of the responses is approximately normally distributed.

a. Find the probability that a response to Energy Star exceeds 43.

b. Find the probability that a response to Energy Star falls between 42 and 45.

c. If you observe a response of 35 to an ecolabel, do you think it is likely that the ecolabel was Energy Star? Explain.

Find az-score, call itz0, such that

a.P(z鈮�z0)=.5080

b.P(z鈮�z0)=.5517

c.P(z鈮�z0)=.1492

d.P(z0鈮�z鈮�.59)=.4773

Variable speed limit control for freeways. A common transportation problem in large cities is congestion on the freeways. In the Canadian Journal of Civil Engineering (January 2013), civil engineers investigated the use of variable speed limits (VSL) to control the congestion problem. A portion of an urban freeway was divided into three sections of equal length, and variable speed limits were posted (independently) in each section. Probability distributions of the optimal speed limits for the three sections were determined. For example, one possible set of distributions is as follows (probabilities in parentheses). Section 1: 30 mph (.05), 40 mph (.25), 50 mph (.25), 60 mph (.45); Section 2: 30 mph (.10), 40 mph (.25), 50 mph (.35), 60 mph (.30); Section 3: 30 mph (.15), 40 mph (.20), 50 mph (.30), 60 mph (.35).

  1. Verify that the properties of a discrete probability distribution are satisfied for Section 1 of the freeway.
  2. Repeat part a for Sections 2 and 3 of the freeway.
  3. Find the probability that a vehicle traveling at the speed limit in Section 1 will exceed 30 mph.
  4. Repeat part c for Sections 2 and 3 of the freeway.

Safety of underground tunnels. Research published in the journal Tunnelling and Underground Space Technology (July 2014) evaluated the safety of underground tunnels built in rigid soils. A factor of safety (FS), measured as the ratio of capacity over demand, was determined for three different areas of tunnels made from shotcrete: tunnel face, tunnel walls, and tunnel crown. FS was determined to be normally distributed in each area, with means and standard deviations shown in the table. Tunnel failure is considered to occur when FS is lower than or equal to 1. Which tunnel area is more likely to result in failure? Why?


Mean

Standard Deviation

Tunnel Face

1.2

0.16

Tunnel Walls

1.4

0.2

Tunnel Crown

2.1

0.7

Consider the probability distribution shown here

  1. Calculate 渭,蟽2补苍诲蟽.
  2. Graph p(x). Locate渭,渭鈭�2蟽补苍诲渭+2蟽 on the graph.
  3. What is the probability that x is in the interval 渭+2蟽 ?
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