Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,300. 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.

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 19 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 123 points? (Round your answer to five decimal places.)

Answer 1

1) Given   = $44,000

standard deviation = $6,300

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

Let the 90^th percentile for an individual teacher's salary = X

P((X-)/) = 0.9

From the normal table the z-score for 90 th percentile = 1.285

(X-)/ = 1.285

X = 44000+ 1.285*6300 = $52,095.5 = $52,096

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

sample of 10 individuals follow N($44,000 , 6300/) = N($44,000 , 1992.2)

P((-)/^') = 0.9

= 44000 + 1992.2*1.285 = $46,560

2)

Given   = 105

standard deviation = 20

sample size = 19

sample follows a distribution of N (105 , 4.58831)

P(85 < X < 123)

Z = (-)/

for = 85 , Z = (85 - 105)/4.58831

for = 123 ,  Z = (123 - 105)/4.58831

P(85 < X < 123) = 0.99995