New book reviews. In Exercise 2.181 (p. 99), you read about a study of book reviews...

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.

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.