According to the web site www.torchmate.com, "manhole covers must be a minimum of 22in. in diameter, but can be as much as 60in. in diameter." Assume that a manhole is constructed to have a circular opening with a diameter of 22in. Men have shoulder breadths that are normally distributed with a mean of 18.2in. and a standard deviation of 1.0in. a) What percentage of men will fit into the manhole? b) Assume that the Connecticut Light and Power company employs 36 men who work in the manholes. If 36 men are randomly selected, what is the probability that their mean shoulder breadth is less than 18.5in.? Does this suggest that money can be saved by making smaller manholes with a diameter of 18.5in.? Why or why not?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
According to the web site www.torchmate.com, "manhole covers must be a minimum of 22in. in diameter, but can be as much as 60in. in diameter." Assume that a manhole is constructed to have a circular opening with a diameter of 22in. Men have shoulder breadths that are
a) What percentage of men will fit into the manhole?
b) Assume that the Connecticut Light and Power company employs 36 men who work in the manholes. If 36 men are randomly selected, what is the probability that their mean shoulder breadth is less than 18.5in.? Does this suggest that money can be saved by making smaller manholes with a diameter of 18.5in.? Why or why not?
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