Business and Society (March 2011) published a study on the sustainability behaviors of CPA corporations. The level of support senior managers have for corporate sustainability, business practices designed around social and environmental considerations, was measured quantitatively on a scale ranging from 0 to 160 points, where higher point values indicate a higher level of support for sustainability. The study provided the following information on the distribution of levels of support for sustainability: µ = 68, ? = 27. Now consider a random sample of 45 senior managers and let represent the sample mean level of support.
a. Give the value of , the mean of the sampling distribution of , and interpret the result.
b. Give the value of , the standard deviation of the sampling distribution of , and interpret the results.
c. What does the Central Limit Theorem say about the shape of the sampling distribution of ?
d. Find P( > 65).