in a survey of women in a certain country ages 2029 the heig

in a survey of women in a certain country ages 20-29, the height was 63.9 inches with a standard deviation of 2.92 inches. what height represents the 95th percentile, what hewight represents the first quartile

Solution

what height represents the 95th percentile

P(X<x)=0.95

--> P((X-mean)/s <(x-63.9)/2.92) = 0.95

--> P(Z<(x-63.9)/2.92) = 0.95

--> (x-63.9)/2.92 = 1.64 (from standard normal table)

So x= 63.9 +1.64*2.92 =68.6888

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what hewight represents the first quartile

P(X<x)=0.25

--> P((X-mean)/s <(x-63.9)/2.92) = 0.25

--> P(Z<(x-63.9)/2.92) = 0.25

--> (x-63.9)/2.92 = -0.67 (from standard normal table)

So x= 63.9 -0.67*2.92 =61.9436