Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district.

1. Find the 90^th percentile for an individual teacher’s salary.
2. Find the 90^th percentile for the average teacher’s salary.

Answer 1

1)

mean μ=	44000.000
standard deviation σ=	6500.000

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=44000+1.28*6500=			$ 46773.33

2)

mean μ=

44000.000

sample size       =n=	10
std error=σx̅=σ/√n=	2055.4805

for 90th percentile critical value of z=		1.28
therefore corresponding value=mean+z*std deviation=44000+1.28*2055.4805=			$ 46631.02