Please show steps The height of adult women in the United St

Please show steps

The height of adult women in the United States can be approximated by a normal distribution with a mean of 65 inches and a standard deviation of 3 inches. approximate the height at which 25% of the women are shorter and 75% are taller.

Solution

P(X<c)=0.25

--> P((X-mean)/s <(c-65)/3) = 0.25

--> P(Z<(c-65)/3)=0.25

--> (c-65)/3 =-0.67 (from standard normal table)

So c= 65-0.67*3=62.99