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Most powerful American women. Refer to the Fortune (Oct. 16, 2008) list of the 50 most powerful women in America. In Exercise 5.39 (p. 242), you assumed that the ages (in years) of these women are approximately normally distributed. A MINITAB printout with summary statistics for the age variable saved in the WPOWER50 file is reproduced below.
a. Use the relevant statistics on the printout to find the interquartile range IQR.
b. Locate the value of the standard deviation s on the printout.
c. Use the results from parts a and b to demonstrate that the age distribution is approximately normal. d. Construct a relative frequency histogram for the age data. Use this graph to support your assumption of normality.
Exercise 5.39
Most powerful American women. Refer to the Fortune (Oct. 16, 2008) list of the 50 most powerful women in America, presented in Exercise 2.60 (p. 57). Recall that the data on age (in years) of each woman is stored in the WPOWER50 file. The ages in the data set can be shown to be approximately normally distributed with a mean of 50 years and a standard deviation of 6.4 years. A powerful woman is randomly selected from the data, and her age is observed.
a. Find the probability that her age will fall between 55 and 60 years.
b. Find the probability that her age will fall between 48 and 52 years.
c. Find the probability that her age will be less than 35 years.
d. Find the probability that her age will exceed 40 years.
e. A 25-year-old woman claims she is one of the 50 most powerful women. Do you believe her? Explain.
Exercise 2.60
Most powerful businesswomen in America. Fortune (Oct. 16, 2008) published a list of the 50 most powerful women in business in the United States. The data on age (in years) and title of each of these 50 women are stored in the WPOWER50 file. The first five and last five observations of the data set are listed in the table below. Descriptive statistics for the ages are displayed on the MINITAB printouts (p. 58).
a. Find the mean, median, and modal age of these 50 women on the printout. Interpret these values.
b. What do the mean and median indicate about the skewness of the age distribution?
c. Find the modal age class on the histogram
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