New book reviews. In Exercise 2.181 (p. 99), you read about a study of book reviews in American history, geography, and area studies published in Choice magazine ( Library Acquisitions: Practice and Theory , Vol. 19, 1995). The overall rating stated in each review was ascertained and recorded as follows: 1 = would not recommend, 2 = cautious or very little recommendation, 3 = little or no preference, 4 = favorable/recommended, 5 = outstanding/ significant contribution. Based on a sample of 375 book reviews, the probability distribution of rating, x , follows.
Booking Rating x | p(x) |
1 | .051 |
2 | .099 |
3 | .093 |
4 | .635 |
5 | .122 |
a. Is this a valid probability distribution?
b. What is the probability that a book reviewed in Choice has a rating of 1?
c. What is the probability that a book reviewed in Choice has a rating of at least 4?
d. What is the probability that a book reviewed in Choice has a rating of 2 or 3?
e. Find E(x).
f. Interpret the result, part e .
Exercise 2.181
Best-paid CEOs. Refer to the Forbes list of the 40 bestpaid chief executive officers, Best-paid CEOs. Forbes magazine conducts an annual survey of the salaries of chief executive officers. In addition to salary information, Forbes collects and reports personal data on the CEOs, including their level of education and age. Do most CEOs have advanced degrees, such as master’s degrees or doctorates? The data in the accompanying table (saved in the FORBES40 file) represent the highest degree earned by each of the top 40 best-paid CEOs of 2010. Use a graphical method to summarize the highest degree earned by these CEOs. What is your opinion about whether most CEOs have advanced degrees?. The salary and age of each CEO are saved in the FORBES40 file.
*a. Use a graph to portray the relationship between a CEO’s salary and age. Do you detect a trend?
b. According to Chebyshev’s rule, what percentage of the age measurements would you expect to find in the intervals x ± .75s, x ± 2.5s, and x ± 4s ?
c. What percentage of the age measurements actually fall into the intervals of part b? Compare your results with those of part b .
d. Repeat parts b and c for salary.
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