Question

QUESTION 11 5 points Save Answer Use the information below answer the next 2 questions: 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. (a). Find the 90th percentile for an individual teacher's salary. QUESTION 12 5 points Save Answer (b) Find the 90th percentile for the average teacher's salary

Answer 1

Solution:-

Given that,

mean = $\mu$ = 44000

standard deviation = $\sigma$ = 6500

a) Using standard normal table,

P(Z < z) = 90%

= P(Z < z) = 0.90  

= P(Z < 1.282) = 0.90

z = 1.282

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.282 * 6500 + 44000

x =$ 52333

b) n = 10

$\mu$_{$\bar x$} =  $\mu$ = 44000

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 6500 / $\sqrt$ 10 = 2055.48

Using z-score formula  

$\bar x$ = z * $\sigma$ _{$\bar x$}+ $\mu$ _{$\bar x$}

$\bar x$ = 1.282 * 2055.48 + 44000

$\bar x$ = $ 46635