The U.S. Air Force requires that pilots have heights between 64 inc. and 77 in. The heights of women are normally distributed with mean 63.7 in. and standard deviation 2.9 in. (a) Find the percentage of women meeting the height requirement. (b) If the Air Force changes its policy to admit all women taller than the lowest 4%, what is the new lower height requirement?
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!
The U.S. Air Force requires that pilots have heights between 64 inc. and 77 in.
The heights of women are
in.
(a) Find the percentage of women meeting the height requirement.
(b) If the Air Force changes its policy to admit all women taller than the lowest 4%, what is
the new lower height requirement?
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