Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $42,000 and a standard deviation of $5,700. 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

Solution:-

Given that,

mean = = $ 42000

standard deviation = = $ 5700

Using standard normal table,

P(Z < z) = 90%

= P(Z < z) = 0.90  

= P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 5700 + 42000

x = $ 49296

b) n = 10

= = $ 42000

= / n = 5700 / 10 = 1802.50

Using z-score formula  

= z * +

= 1.28 * 1802.50 + 42000

= $ 44307