SOLUTION: 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 require very wide seats that wo

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Question 1167479: 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 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 and a standard deviation of 1.1 in. Find P99. That​ is, find the hip breadth for men that separates the smallest 99​% from the largest 1​%.
Need to find
the hip breadth for men that separates the smallest 99​% from the largest 1​% is P99 in.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you have a mean of 14.6 and a standard deviation of 1.1.

you want to find the z-score that has an area to the left of it of .99

then you want to find the raw score.

you would look into the following z-score table if you didn't have one of your own.

https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

you would look for an area to the left of the z-score of.99

you will probably not find it, but you will get close.

i looked in the table and found:

an area of .98983 to the left of a z-score of 2.32.
an area of .99010 to the left of a z-score of 2.33.

since .99 is closer to .99010 than to .98983, then you would pick a z-score of 2.33.

you would then use the z-score formula to find the raw score associated with that.

the z-score formula is z = (x - m) / s

z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation in this case.

the formula becomes 2.33 = (x - 14.6) / 1.1

solve for x to get x = 2.33 * 1.2 + 14.6 = 17.163.

if the width of the seats is 17.163 inches, than 99% of the males will fit in them.

there is an online calculator that will show you what this looks like.

that calculator can be found at http://davidmlane.com/hyperstat/z_table.html

here's what the calculator shows.









the first one looks for the area to the left of a z-score of 2.33.

the second one looks for the area to the left of a raw score of 17.163

the third looks for the z-score associated with an area of .99 to the left of it.

the fourth looks for the raw score associated with an area of .99 to the left of it.

the calculator gives a more detailed for an area of .99 to the left of it.

the z-score was 2.326 and the raw score was 17.159.

if you used this calculator, that's what your answer would have been.

you could also have interpolated from the table and gotten 2.326 z-score as well, but, why bother when the calculator can do the hard work for you?

either answer is acceptable, depending on how detailed the answer needs to be.

there are other calculators that will give you an even more detailed answer.
in most cases, going further than 2 or 3 decimal places with the z-score is not necessary.