Question

A ski resort pays its part-time seasonal employees on an hourly basis. At a certain mountain, the hourly rates have a normal distribution with σ = $3.00. If 20 percent of all part-time seasonal employees make more than $13.16 an hour, what is the average hourly pay rate at this mountain? (Round your answer to 2 decimal places.)

Answer 1

Answer:

The average hourly pay is $10.64

Explanation:

To calculate probabilities in an easy way we convert our values (x=hourly pay in this case) to standard values (a normal distribution with mean = 0 and σ =) which are tabulated, every z-score with the accumulated probability to the left. It is done according to this formula:

$\mbox{z-score}=\frac{x-\mu_{x} }{ \sigma_{x} }$

To find the mean ($\mu_{x}$), we are going to calculate the equivalent z-score to $13.16, working out an equation in which the average is going to be the only incognite. This z-score is the one where we have 20% of area to the right (x higher than 13.16) and 80% to the left (x lower than 13.16):

$\mbox{z-score}=0.8416=\frac{13.16-\mu_{x} }{ 3 }\\\\0.8416*3=13.16-\mu_{x}\\\\\mu_{x}=13.16-0.8416*3=10.64$