Question

Suppose that in a certain Senior High School the average height of male students is 155.9 cm with standard deviation of 20.4 cm. If you choose 40 students what is the probability that their height is above 155 cm?

Answer 1

Let $X=$ the height of male student in sample: $X\sim N(\mu, \sigma^2/n).$

Given $\mu=155.9\ cm, \sigma=20.4\ cm, n=40.$

$$P(X>155)=1-P(X\leq 155)$$

$$=1-P(Z\leq\dfrac{155-155.9}{20.4/\sqrt{40}})\approx1-P(Z\leq-0.279)$$

$$\approx0.6099$$