Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100% of males would requi seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.1 in That is, find the hip breadth for men that separates the smallest 99% from the largest 1%. The hip breadth for men that separates the smallest 99% from the largest 1% is Pg9 = in. (Round to one decimal place as needed.)
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!
![### Designing Aircraft Seats for Optimal Fit
Engineers aim to design seats in commercial aircraft that can accommodate 99% of all males. Creating seats to fit 100% of males is not feasible due to the excessive width that would be required. Males have hip breadths that follow a normal distribution with a mean of 14.4 inches and a standard deviation of 1.1 inches. To find the optimal seat width, we calculate the hip breadth that separates the smallest 99% from the largest 1%.
#### Problem Statement:
Find the hip breadth for men that separates the smallest 99% from the largest 1%. This is represented as \(P_{99}\).
`The hip breadth for men that separates the smallest 99% from the largest 1% is \( P_{99} = \boxed{\text{____}} \) inches.`
*Round to one decimal place as needed.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab0e5d97-7b6b-46cc-bf12-d986af136b0a%2F859f7e76-880e-4414-bc6e-82cb4ccb84f5%2Fdtb4fs6_processed.jpeg&w=3840&q=75)
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