Suppose that giraffe heights follow a normal distribution wi

Suppose that giraffe heights follow a normal distribution with mean 18

a.) how tall must a giraffe be to be in the top 15% of giraffes?

P(X>c)=0.15

--> P((X-mean)/s <(c-18)/2.5) =1-0.15=0.85

--> P(Z<(c-18)/2.5) =0.85

--> (c-18)/2.5= 1.04 (from standard normal table)

So c= 18+1.04*2.5=20.6

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b) what range of heights (low - high) mark off the middle 60% of giraffe heights?

Given a=1-0.6=0.4, Z(0.4/2)=Z(0.2)=0.84 (from standard normal table)

So the lower value is

mean -Z*s =18-0.84*2.5 =15.9

So the high value is

mean + Z*s =18+0.84*2.5 =20.1

So the range = 20.1- 15.9 =4.2