A Health company provides compensation information on more than 170 benchmark po

Question

A Health company provides compensation information on more than 170 benchmark positions in human resources. The october 2003 posting indicated that labor leation managers earn a mean annual salary of $86,700. Assume that annual slaries are normally distributed and have a standard deviation of $8850.
a. What is the probability that a randomly selected labor relation manager earned more than $100,000 in 2003?
b. A sample of 20 labor relation managers is taken, and annual salaries are reported. What is the probability that the sample mean annual salary falls between $80,00 and $90,000?

thanks for your help

Explanation / Answer

Given X~Normal(=86,700, s=8850)

a. What is the probability that a randomly selected labor relation manager earned more than $100,000 in 2003?

P(X>100000) = P((x-)/s > (100000-86700)/8850)

=P(Z>1.5)

=0.0668 (check standard normal table)

----------------------------------------------------------------------------------------------------------------------------

b. A sample of 20 labor relation managers is taken, and annual salaries are reported. What is the probability that the sample mean annual salary falls between $80,00 and $90,000?

P(80000 <xbar < 90000) = P((80000-86700)/(8850/sqrt(20)) <(xbar-)/(s/n) < (90000-86700)/(8850/sqrt(20)))

=P( -3.39<Z< 1.67)

= 0.9522 (check standard normal table)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.