A recent Gallup study (http://www.gallup.com/poll/175286/hour-workweek-actually longer seven hours.aspx) found the typical American works an average of 46.7 hour per week. The study did not report the shape of the distribution of hours worked or the standard deviation. It did however indicate that 40% of the workers worked less than 40 hours a week and that 18 percent worked more than 60 hours.
a. If we assume that the distribution of hours worked is normally distributed, and knowing 40% of the workers worked less than 40 hours, find the standard deviation of the distribution.
b. If we assume that the distribution of hours worked is normally distributed and 18% of the workers worked more than 60 hours, find the standard deviation of the distribution.
c. Compare the standard deviations computed in parts a and b. Is the assumption that the distribution of hours worked is approximately normal reasonable? Why?