A survey found that women's heights are normally distributed with mean 63.5 in. and standard deviation 3.7 in. The survey als found that men's heights are normally distributed with mean 67.4 in. and standard deviation 3.1 in. Consider an executive jet seats six with a doorway height of 56.4 in. Complete parts (a) through (c) below. a. What percentage of adult men can fit through the door withbut bending? The percentage of men who can fit without bending is %. (Round to two decimal places as needed.) b. Does the door design with a height of 56.4 in. appear to be adequate? Why didn't the engineers design a larger door? O A. The door design is inadequate, because every person needs to be able to get into the aircraft without bending. There no reason why this should not be implemented. B. The door design is inadequate, but because the jet is relatively small and seats only six people, a much higher door would require major changes in the design and cost of the jet, making a larger height not practical.

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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!