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Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% 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 13.9 in. and a standard deviation of 0.8 in. Find Pao. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%.

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% 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 13.9 in. and a standard deviation of 0.8 in. Find Pao. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 18HP
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Question Help Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% 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 13.9 in. and a standard deviation of 0.8 in. Find P90. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%. Use technology to find the z-score corresponding to the given area. Then use the fact that x = µ + (z•o) to find the hip breadth associated with the given area. The 90th percentile, P90, means that 90% of the data is less than the random variable x. That is, the area under the normal curve to the left of x is equal to 0.9000. Area = 0.90 13.9 Now use technology to find the z-score that corresponds to the shaded area, 0.9000, rounding to two decimal places. z= 1.28
Transcribed Image Text:Question Help Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% 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 13.9 in. and a standard deviation of 0.8 in. Find P90. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%. Use technology to find the z-score corresponding to the given area. Then use the fact that x = µ + (z•o) to find the hip breadth associated with the given area. The 90th percentile, P90, means that 90% of the data is less than the random variable x. That is, the area under the normal curve to the left of x is equal to 0.9000. Area = 0.90 13.9 Now use technology to find the z-score that corresponds to the shaded area, 0.9000, rounding to two decimal places. z= 1.28
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