Most powerful American women. Refer to the Fortune (Nov. 14,2005) list of the 50 most powerful women in America, presented in Exercise 2.58 (p. 59). 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 5.3 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.
Exercise 2.58
Most powerful women in America. Fortune (Nov. 14, 2005) published a list of the 50 most powerful women in America. 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 two observations of the data are listed in the accompanying table.
a. Find the mean, median, and modal age of these 50 women.
b. What do the mean and median indicate about the skewness of the age distribution?
c. Construct a relative frequency histogram for the age data. What is the modal age class?
WPOWER50 (Selected observations)
Rank | Name | Age Company | Title | |
1 | Meg Whitman | 49 | eBay | CEO/Chair |
2 | Anne Mulcahy | 52 | Xerox | CEO/Chair |
3 | Brenda Barnes | 51 | Sara Lee | CEO/President |
4 | Oprah Winfrey | 51 | Harpo | Chair |
5 | Andrea Jung | 47 | Avon | CEO/Chair |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
49 | Safra Catz | 43 | Oracle | President |
50 | Kathy Cassidy | 51 | General Electric | Treasurer |
Source: Fortune, Nov. 14, 2005.
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