lets come up with sitting distance which is the length from the front of the sea

Question

lets come up with sitting distance which is the length from the front of the seat cushion to the back seat in front of it. to design this we must consider buttock to knee lengths that are normally distributed with am mean of 23.5 and standard deviation of 1.1 inches. find the maximum buttock to knee length that you are willing to accomadate. womens buttock to knee lengths are normally distrubted with a mean of 22.7 inches and standard deviation of 1 inch. what percentage of women would be able to fit in these seats, based pm their buttocks to knee lengths? how much extra room would you add

Explanation / Answer

here level of significance is not given , let it be 5%

answer of part 1)mean=23.5 , standard deviation=sd=1.1

margin of error=z(.05)*sd=1.96*1.1=2.156

maximum buttock to knee length that willing to accomadate=mean+margin of error=23.5+2.156=25.656

answer of part 2)

here we use standard normal variate z=(x-mean)/sd

for woman mean=22.7 ,sd=1

for x=25.656, z=(25.656-22.7)/1=2.956

P(X<25.656)=P(z<2.956)=0.9984

so 0.9984 *100=99.84% women would be able to fit in these seats

answer for third) to get the answer of this part there is need of more information, e.g % of level of significance

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