Designing Manholes According to the web site wwwtorchmatecom

Designing Manholes According to the web site www.torchmate.com, \"manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. in diameter.\" Assume that a manhole is constructed to have a circular opening with a diameter of 22 in. Men have shoulder breadths that are normally distributed with a mean of 18.2 in. and a standard deviation of 1.0 in. (based on data from the National Health and Nutrition Examination Survey). What percentage of men will fit into the manhole? Assume that the Connecticut Light and Power Company employ 36 men who work in manholes. If 36 men are randomly selected, what is the probability that their mean should breadth is less than 18.5 in.? Does this result suggest that money can be saved by making smaller manholes with a diameter of 18.5 in.? Why or why not?

Solution

If X is the average shoulder breadth of men then mu = 18.2 and sigma = 1

a) Proportion of men fit = Prob (x<22) =

P(Z<3.2) = 1.000

Hence almost 100% men will fit

b) n = 36

Std error = 1/6

Prob (X<18.5) = P(Z<0.3(6)) = P(Z<1.8) = 0.9641

Hence 96.41% will fit

Yes money can be saved as 96.41% fit into this.