a recent study found that hourly wages eaned by employees po

a recent study found that hourly wages eaned by employees possesing a Master\'s degree are distributed normally with a mean of $27.50 and a standard deviation of $3.50.

1- Haily just started a new job earning $34.64 an hour. Find and interpret the precentile for Haily\'s earning?

Solution

Mean = 27.50$

Standard Deviation = 3.50$

We need to find the Z value, in order to find the percentile for Haily\'s earning

Z = (X - mean)/sigma

X = 34.64$, mean = 27.50 and standard deviation = 3.50

Z = (34.64 - 27.50)/(3.50) = 2.04

Hence we need to find the population that has Z value greater than 2.04

P(Z>2.04) = 1 - P(Z<2.04) = 1 - 0.979 = 0.021

Hence the percentile score is 97.9%, since only 2.1% people are having greater earnings than hailey