Question

Salaries at an organization are normally distributed with a mean of µ = $50,000 with a standard deviation of σ = $15,000. What is the probability of selecting a sample of 40 people with a mean salary of less than $40,000? Which statistic should you use to answer this question?

Answer #1

**z statistic will be used because population std dev is
given.**

µ = 50000

σ = 15000

n= 40

X = 40000

Z = (X - µ )/(σ/√n) = ( 40000
- 50000.00 ) / (
15000.000 / √ 40 )
= -4.22

P(X < 40000 ) = P(Z < -4.216 )
= 0.000012 (answer)

excel formula for probability from z score is
=NORMSDIST(Z)

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