Math Statistics

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% are huge successes, 30% are modest successes, 40% break even, and 10% are losers. However, before a publishing decision is made, the book will be reviewed. In the past, 99% of the huge successes received favorable reviews, 70% of the moderate successes received favorable reviews, 40% of the break-even books received favorable reviews, and 30% of the losers received favorable reviews. Complete parts (a) and (b).

a. 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 = ???

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

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

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

b. What proportion of textbooks receives favorable​ reviews?

The proportion of textbooks that receive a favorable reviews is = ???

Answer 1

We're given the distribution of the types of books availabe, so we can determine the total percentage of books that receive favorable reviews and then compare it to the total percentage of books that receive positive reviews that were a huge success or other category.

To do this, we need to multiply each category by the percentage of those books that received positive reviews:

99%*20% + 70%*30% + 40%*40% + 30%*10% = 59.8%

So this tells us the total percentage of books that receive positive reviews. The percentage of books that are hugely successful and receive positive reviews is simply 99%*20%, which is equal to 19.8% of total books.

So since we assume the book has a positive review, it will be a 19.8%/59.8% chance to be a huge success, or 33.11%

The questions in the rest of part A are answered similarily!

For part B, the answer is contained above.