Answer
a) $2.28\%$
b) $39.9$ inches
c) $0.9234$
Work Step by Step
a) We find the value of z:
$z=\frac{2.8}{1.4}=2$
Hence, using a table of z-scores, we see that $2.28\%$ of men are under $38.8$ inches in sitting height.
b) We know that the value of z must be equal to $2.05$ so that $98\%$ of men are accommodated. Hence:
$h=(1.4)(2.05)+36=39.87≈39.9$
c. We find the value of z:
$z=\frac{1}{(1.4)(.5)}=1.429$
Using an exact value finder given z, we find that the corresponding probability is $0.9234$.
