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 = $4.00

If 15 percent of all part-time seasonal employees make more than $19.22 an hour, what is the average hourly pay rate at this mountain? (Round your answer to 2 decimal places.)

Answer 1

X ~ N( , ²)

We convert this to standard normal as

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

We have to calculate sucn that P( X > 19.22) = 0.15

That is

P( Z > 19.22 - / 4) = 0.15 (We converted the expression as standard normal using formula above)

P( Z < 19.22 - / 4) = 0.85

From the Z table, z-score for the probability of 0.85 is 1.0365

So,

19.22 - / 4 = 1.0365

Solve for

19.22 - = 4 * 1.0365

= 19.22 - 4 * 1.0365

= 15.074

Average hourly pay rate at this mountain = $15.07 (Rounded to two decimal)