Question

Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a normal distribution with σ = $6.00. If 23 percent of all part-time seasonal employees make more than $13.14 an hour, what is the average hourly pay rate at this mountain? (Round your answer to 2 decimal places.)

what is the Average hourly pay rate?

Answer 1

Given,

= 6 , = ?

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

We have to calculate such that,

P(X > 13.14) = 0.23

P(Z > (13.14 - ) / 6 ) = 0.23

P(Z < (13.14 - ) / 6) = 1 - 0.23

P(Z < (13.14 - ) / 6) = 0.77

From Z table, z-score for the probability of 0.77 is 0.7388

(13.14 - ) / 6) = 0.7388

Solve for

= 8.71