In Exercises 21–24, use these parameters (based on Data Set 1 “Body Data” in Appendix B): Men’s heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in. Mickey Mouse Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as Mickey Mouse characters? b. If the height requirements are changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?
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!
In Exercises 21–24, use these parameters (based on Data Set 1 “Body Data” in Appendix B):
- Men’s heights are
normally distributed with mean 68.6 in. and standard deviation 2.8 in. - Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.
Mickey Mouse Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as Mickey Mouse characters?
b. If the height requirements are changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?
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