1 answer

QUESTION 11 5 points Save Answer Use the information below answer the next 2 questions: Salaries...

Question:

QUESTION 11 5 points Save Answer Use the information below answer the next 2 questions: Salaries for teachers in a particular

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

Answers

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

.

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