The editor of a textbook publishing company is trying to decide whether to publi

Question

The editor of a textbook publishing company is trying to decide whether to publish a proposed business statistics textbook. Information on previous textbooks published indicate that 20 %20% are huge successes, 30 %30% are modest successes, 30 %30% break even, and 20 %20% are losers. However, before a publishing decision is made, the book will be reviewed. In the past, 97 %97% of the huge successes received favorable reviews, 60 %60% of the moderate successes received favorable reviews, 40 %40% of the break-even books received favorable reviews, and 20 %20% of the losers received favorable reviews. Complete parts (a) and (b).

If the proposed textbook receives a favorable review, how should the editor revise the probabilities of the various outcomes to take this information into account?

The probability that if the proposed textbook receives a favorable review, the book will be a huge success is

(Round to three decimal places as needed.)

The probability that if the proposed textbook receives a favorable review, the book will be a modest success is

(Round to three decimal places as needed.)

The probability that if the proposed textbook receives a favorable review, the book will break even is

(Round to three decimal places as needed.)

The probability that if the proposed textbook receives a favorable review, the book will be a loser is

(Round to three decimal places as needed.)

b. What proportion of textbooks receives favorable reviews?

The proportion of textbooks that receive a favorable reviews is

(Round to three decimal places as needed.)

Explanation / Answer

a) P(favorable review) = 0.2 * 0.97 + 0.3 * 0.6 + 0.3 * 0.4 + 0.2 * 0.2 = 0.534

P(huge success| favorable review) = P(favorable review | huge success) * P(favorable review)

                                                = 0.97 * 0.534 = 0.518

P(modest | favorable) = P(favorable | modest) * P(favorable) = 0.6 * 0.534 = 0.320

P(break even | favorable) = P(favorable | break even) * P(favorable) = 0.4 * 0.534 = 0.214

P(losers | favorable) = P(favorable | losers) * P(favorable) = 0.2 * 0.534 = 0.107

b) P(favorable reviews) = 0.2 * 0.97 + 0.3 * 0.6 + 0.3 * 0.4 + 0.2 * 0.2 = 0.534

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