Men’s heights are normally distributed with a mean of 69.0 inches, and a standard deviation of 2.8 inches. The Mark VI monorail at Disneyworld has a door height of72 inches. a. What doorway height would allow 98% of men to walk through without bending? b. If a random sample of 100 men is taken, what is the chance their average height is at least 70.0 inches? c. What percent of all men have a height of at least 67.0hinches?
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!
Men’s heights are
a. What doorway height would allow 98% of men to walk through without bending?
b. If a random sample of 100 men is taken, what is the chance their average height is at least 70.0 inches?
c. What percent of all men have a height of at least 67.0hinches?
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