Chapter 5.3, Problem 5.25ACB

Corporate sustainability of CPA firms. Refer to the Business and Society (March 2011 ) study on the sustainability behaviors of CPA corporations, Exercise 1.28 (p. 27). Corporate sustainability, recall, refers to business practices designed around social and environmental considerations. The level of support senior managers have for corporate sustainability was measured quantitatively on a scale ranging from 0 to 160 points. The study provided the following information on the distribution of levels of support for sustainability: µ = 68, σ = 27. Now consider a random sample of 45 senior managers and let x represent the sample mean level of support.

1. a. Give the value of ${\mu }_{\bar{x}}$, the mean of the sampling distribution of $\bar{x}$, and interpret the result.
2. b. Give the value of ${\sigma }_{\bar{x}}$, the standard deviation of the sampling distribution of $\bar{x}$, and interpret the result.
3. c. What does the Central Limit Theorem say about the shape of the sampling distribution of $\bar{x}$?
4. d. Find $P\left(\bar{x}\succ 65\right)$.