Chapter 5.3, Problem 5.24ACB

Salary of a travel management professional. According to the most recent Global Business Travel Association (GBTA) survey, the average base salary of a U.S. travel management professional is $94,000. Assume that the standard deviation of such salaries is $30,000. Consider a random sample of 50 travel management professionals and let x represent the mean salary for the sample.

1. a. What is ${\mu }_{\bar{x}}$?
2. b. What is ${\sigma }_{\bar{x}}$?
3. c. Describe the shape of the sampling distribution of $\bar{x}$.
4. d. Find the z-score for the value $\bar{x}=86,660$.
5. e. Find $P\left(\bar{x}\succ 86,660\right)$.