Although the standard workweek is 40 hours a week many
Although the standard workweek is 40 hours a week, many people work a lot more than 40 hours
a week. The following data give the numbers of hours worked last week by 50 people.
a. The sample mean and sample standard deviation for this data set are 49.012 and 5.080, respectively. Using Chebyshev’s theorem, calculate the intervals that contain at least 75%, 88.89%, and 93.75% of the data.
b. Determine the actual percentages of the given data values that fall in each of the intervals that you calculated in part a. Also calculate the percentage of the data values that fall within one standard deviation of the mean.
c. Do you think the lower endpoints provided by Chebyshev’s theorem in part a are useful for this problem? Explain your answer.
d. Suppose that the individual with the first number (54.4) in the fifth row of the data is a workaholic who actually worked 84.4 hours last week and not 54.4 hours. With this change now and Recalculate the intervals for part a and the actual percentages for part b. Did your percentages change a lot or a little?
e. How many standard deviations above the mean would you have to go to capture all 50 data values? What is the lower bound for the percentage of the data that should fall in the interval, according to the Chebyshev theorem.
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