(b) A recent Gallup study found the typical American works an average of 46.7 hours per week. The study did not report the shape of the distribution of hours worked or the standard deviation. It did, however, indicate that 411% of the workers worked Eess than 40 hours a week and that 18 percent worked more than 60 hours. 1 8"? (i) If we assume that the distribution of hours worked is normally distributed, A/ (\"J ' and knowing 40% of the workers worked less than 40 hours, nd the standard deviation of the distribution. (4 marks) (ii) If we assume that the distribution of hours worked is normally distributed, and 18% of the workers worked more than 60 hours, nd the standard deviation of the distribution. (4 marks) (iii) Compare the standard deviations computed in parts (i) and (ii). Discuss whether the assumption that the distribution of hours worked is approximately normal is reasonable. (4 marks)