Normally distributed height

Question

The heights of 18 year-old men are approximately normally distributed, with mean 66 inches and standard deviation 4 inches.

(a) If a random sample of sixteen 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Use 3 decimal places.)

Answer 1

P(65<X<67)

= P[(65-66)/4 < Z < (67-66)/4]

= P(-0.25<Z<0.25)

= 2*P(Z>0.25)

= 2(1-0.5987)

= 2(0.4013)

= 0.8026

≈ 0.803

Hope this helped!