?Refer to the Southern Economic Journal (April 2008) rankings of PhD programs in

If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within the following intervals? a. b. 2 c. 3

Consider a sample data set with the following summary statistics: s = 95, = 72, = 195. a. Calculate IQR. b. Calculate IQR/s. c. Is the value of IQR/s approximately equal to 1.3? What does this imply?

Normal probability plots for three data sets are shown on the next page. Which plot indicates that the data are approximately normally distributed?

Examine the sample data in the accompanying table. a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution. b. Compute s for the sample data. c. Find the values of and , then use these values and the value of s from part b to assess whether the data come from an approximately normal distribution. d. Generate a normal probability plot for the data and use it to assess whether the data are approximately normal.

Refer to the Significance (April 2015) study of contestants’ performances on the United Kingdom’s version of the TV show, The Apprentice, Exercise 2.9 (p. 49). Recall that the performance of each of 159 contestants was rated on a 20-point scale. Contestants were also divided into two groups: those who played for a job and those who played for a business partnership. These data (simulated, based on statistics reported in the article) are saved in the accompanying file. Descriptive statistics for each of the two groups of contestants are displayed in the accompanying Minitab printout. a. Determine whether the performance ratings of contestants who played for a job are approximately normally distributed. b. Determine whether the performance ratings of contestants who played for a business partnership are approximately normally distributed.

Understanding the characteristics of rock masses, especially the nature of the fractures, is essential when building dams and power plants. The shear strength of rock fractures was investigated in Engineering Geology (May 12, 2010). The Joint Roughness Coefficient (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 SPSS histogram. Should the engineers use the normal probability distribution to model the behavior of shear strength for rock fractures? Explain.

Scientists at GlaxoSmithKline Medicines Research Center used high-performance liquid chromatography (HPLC) to determine the amount of drug in a tablet produced by the company (Analytical Chemistry, Dec. 15, 2009). Drug concentrations (measured as a percentage) for 50 randomly selected tablets are listed in the table below and saved in the accompanying file. a. Descriptive statistics for the drug concentrations are shown at the top of the XLSTAT printout on the next page. Use this information to assess whether the data are approximately normal. b. An XLSTAT normal probability plot follows. Use this information to assess whether the data are approximately normal.

Refer to the Southern Economic Journal (April 2008) rankings of PhD programs in economics at 129 colleges and universities, Exercise 2.103 (p. 93). Recall that the number of publications published by faculty teaching in the PhD program and the quality of the publications were used to calculate an overall productivity score for each program. The mean and standard deviation of these 129 productivity scores were then used to compute a 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 is shown below. Use the graph to assess whether the data are approximately normal.

Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 4.100 (p. 239). Data on the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) for each of 992 senior managers at CPA firms are saved in the accompanying file. In Exercise 4.100 you assumed that the level of support variable was approximately normally distributed. a. Construct a histogram for the data and use it to evaluate the validity of the normality assumption. b. Obtain the mean and standard deviation for the data and use these statistics to evaluate the validity of the normality assumption. c. Obtain the interquartile range (IQR) for the data and use it to evaluate the validity of the normality assumption. d. Construct a normal probability plot for the data and use it to evaluate the validity of the normality assumption.

Wear-out failure time of electronic components is often assumed to have a normal distribution. Can the normal distribution be applied to the wear-out of used manufactured products, such as colored display panels? A lot of 50 used display panels was purchased by an outlet store. Each panel displays 12 to 18 color characters. Prior to acquisition, the panels had been used for about one-third of their expected lifetimes. The data in the accompanying table (saved in the file) give the failure times (in years) of the 50 used panels. Use the techniques of this section to determine whether the used panel wearout times are approximately normally distributed.

Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 2.110 (p. 101). 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?

Refer to the data on the October 2015 sanitation scores for 196 cruise ships, first presented in Exercise 2.24 (p. 59). The data are saved in the accompanying file. Assess whether the sanitation scores are approximately normally distributed

Refer to the Sport Journal (Winter 2007) article on a method for ranking the driving performance of PGA golfers, Exercise 2.52 (p. 73). Recall that the method incorporates a golfer’s average driving distance (yards) and driving accuracy (percent of drives that land in the fairway) into a driving performance index. Data on these three variables for the top 40 PGA golfers are saved in the accompanying file. Determine which of these variables—driving distance, driving accuracy, and driving performance index—are approximately normally distributed

Refer to the Geographical Analysis (Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.69 (p. 81). Recall that blocks of sandstone were cut into 300 equal-sized slices, and the slices were randomly divided into three groups of 100 slices each. Slices in Group A were not exposed to any type of weathering; slices in Group B were repeatedly sprayed with a 10% salt solution (to simulate wetting by driven rain) under temperate conditions;and, slices in Group C were soaked in a 10% salt solution and then dried (to simulate blocks of sandstone exposed during a wet winter and dried during a hot summer). All sandstone slices were then tested for permeability, measured in milliDarcies (mD). The data for the study (simulated) are saved in the accompanying file. Is it plausible to assume that the permeability measurements in any of the three experimental groups are approximately normally distributed?

The Journal of Open Archaeology Data (Vol. 1, 2012) provided data on the chemical composition of more than 200 pre Columbian gold and gold-alloy artifacts recovered in the archaeological region inhabited by the Muisca of Colombia (a.d. 600–1800). One of many variables measured was the percentage of copper present in the gold artifacts. Summary statistics for this variable follow: mean = 29.94%, median = 19.75%, standard deviation = 28.37%. Demonstrate why the probability distribution for the percentage of copper in these gold artifacts cannot be normally distributed.