Question

A study has shown that 23 % of all college textbooks have a price of $ 95 or higher. It is known that the standard deviation of the prices of all college textbooks is $ 8.50 . Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks? Round your answer to the nearest integer. μ =

Answer 1

μ₀ = 89

Explanation:

A study has shown that 23 % of all College textbook cost 95 $ or more, then if the area under the bell shape curve is 23 % in the right tail, then

z(score ) = 0,74 ( 0,23 ≈ 0,2296 from z table )

Then z(score) = ( x - μ₀ ) / σ

0,74 = ( 95 - μ₀ ) / 8,5

0,74*8,5 = 95 - μ₀

6,29 - 95 = - μ₀

μ₀ = 88,71

μ₀ = 89