11.7k views
3 votes
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 sell is $12.80. if she wants to price her books to sell to the middle 80% range, what should be the miimum and maximum prices of the books? the standard deviation is $0.83

User MaMazav
by
7.5k points

1 Answer

7 votes
To price her books to sell to the middle 80% range, the publisher needs to set the minimum and maximum prices such that 10% of the prices fall below the minimum price and 10% of the prices exceed the maximum price. This leaves 80% of the prices in the middle range.

To find the minimum and maximum prices, we need to use the z-score formula:

z = (x - μ) / σ

where z is the z-score, x is the price, μ is the mean price, and σ is the standard deviation.

To find the z-score corresponding to the 10th and 90th percentiles, we consult a standard normal distribution table and find that:

z_10 = -1.28
z_90 = 1.28

Substituting the given values, we get:

-1.28 = (x - 12.80) / 0.83
1.28 = (x - 12.80) / 0.83

Solving for x, we get:

x = -1.28(0.83) + 12.80 = $11.72 (rounded to the nearest cent) for the minimum price
x = 1.28(0.83) + 12.80 = $13.88 (rounded to the nearest cent) for the maximum price

Therefore, the minimum price should be $11.72 and the maximum price should be $13.88 to sell to the middle 80% range.
User Chickens
by
7.3k points