Expert Answers

1.Benjamin owns a small Internet business. Besides himself, he employs nine other people.
The salaries earned by the employees are given next
in thousands of dollars (Benjamin’s salary is the largest, of course): 30, 30, 45, 50,
50, 50, 55, 55, 60, 75.
a)Determine the mean and median for salary.
b)Business has been good! As a result, Benjamin has a total of $25,000 in bonus pay to distribute to his employees. One option for distributing bonuses is to give each employee  including himself) $2500. Add the bonuses under this plan to the original salaries to create a new data set. Recalculate the mean and median. How do they compare to the originals?
c)As a second option, Benjamin can give each employee a bonus of 5% of his or her original salary. Add the bonuses under this second plan to the original salaries to create a
new data set. Recalculate the mean and median. How do they compare to the originals?
d)As a third option, Benjamin decides not to give his  employees a bonus at all. Instead, he keeps the $25,000 for himself. Use this plan to create a new data set. Recalculate the mean and median. How do they compare to the originals?
2.According to the U.S. Census Bureau, the mean of the commute time to work for a residentof Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of thecommute time is 8.1 minutes to answer the following (use Chebyshev’s rule):
a)What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean?
b)What minimum percentage of commuters in Boston has a commute time within 1.5 standard deviations of the mean?
c)Why are we using Chebyshev’s rule?