standard Deviation

Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $42,000 and a standard deviation of $5,300. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

(a) Find the 90^th percentile for an individual teacher's salary.

(b) Find the 90^th percentile for the average teacher's salary.

Answer 1

90th percentile corresponds to a z-score of 1.645

for x = individual teacher's salary

z = (x - mean)/standard deviation, so

1.645 = (x - 42000)/5300

solve for x

for XBAR = teacher's salary mean

z = (xbar - mean)/(standard deviation/square root of sample size))

1.645 = (xbar - 42000)/(5300/sqrt(10))

solve for xbar