IMA salary survey. Each year, Management Accounting reports the results of a salary survey of the members of the Institute of Management Accountants (IMA). One year, the 2,112 members responding had a salary distribution with a 20th percentile of $35,100, a median of $50,000, and an 80th percentile of $73,000.

a. Use this information to determine the minimum sample size that could be used in next year’s survey to estimate the mean salary of IMA members to within

$2,000 with 98% confidence. [Hint: To estimate s, first apply Chebyshev’s theorem to find k such that at least 60% of the data fall within k standard deviations of m. Then find s ≈ (80th percentile -20th percentile)/2k.]

b. Explain how you estimated the standard deviation required for the calculation of the sample size.

c. List any assumptions you make.