Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.6 in. and a standard deviation of 0.9 in. Find P95. That is, find the hip breadth for men that separates the smallest 95% from the largest 5%.
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!
![**Problem: Designing Aircraft Seats for Hip Breadth**
Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.6 inches and a standard deviation of 0.9 inch. Find \( P_{95} \). That is, find the hip breadth for men that separates the smallest 95% from the largest 5%.
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The hip breadth for men that separates the smallest 95% from the largest 5% is \( P_{95} = \) [ ] inches.
*(Round to one decimal place as needed.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d4281a1-138d-4154-9dd1-3fb4853cf3e0%2F51f4a1b3-b9f3-4357-bd0f-55e976564520%2Ffx7omu4_processed.png&w=3840&q=75)
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