Answer to Question #321395 in Statistics and Probability for Nards

Question

The heights of the population of boys are normally distributed with a mean of 66 inches and a 

standard deviation of 8.9 inches. If a random sample of 40 boys is drawn from this population,

Answer 1

$$P(X>66)=1-P(Z\le\dfrac{66-66}{8.9/\sqrt{40}})$$

$$=1-P(Z\le 0)=0.5$$

$$P(Z>64.5)=1-P(Z\le\dfrac{64.5-66}{8.9/\sqrt{40}})$$

$$\approx1-P(Z\le-1.065936)\approx0.8568$$

$$P(64.5<X<66)=P(Z<\dfrac{66-66}{8.9/\sqrt{40}})$$

$$-P(Z\le\dfrac{64.5-66}{8.9/\sqrt{40}})\approx0.5-0.143226$$

$$\approx0.3568$$