Question

A small publisher wishes to publish self-improvement books. After a survey of the market, the publisher finds that the average cost of the type of book that she wishes to publish is $15.00. If she wants to price her books to sell in the middle 34% range, what should the maximum and minimum prices of the books be? The standard deviation is $0.25 and the variable is normally distributed.

Answer 1

Middle 34% range: means +/- 17% from the mean (50% percentile on a normal distribution)

50% + 17% = 67%
50% - 17% = 33%

So you’re looking for the z scores at the 67th and 33rd percentile

Using a percentile to z score calculator I get

-0.4399
And
0.4399 as the z-scores

For each z-score, set z = (x - mean) / standard deviation and solve for x. Your two x values should be your upper and lower prices for the book.

Answer 2

or using the 68-95-99.7% rule, the middle 68% is 1 standard deviation from the mean
So you should get 15-0.25 and 15+0.25

Answer 3

We want the middle 68%