Question

In a school with 500 students, the average height is 165 +-10 cm. Assuming that the height follows the normal distribution:

If we choose a sample of 25 people from the above school:

What is the probability that a student is taller than 169 cm?

What is the probability that a student is less than 163 cm tall?

Answer 1

Solution:

Given, $\mu=165,\sigma=10,n=25$

$X\sim N(\mu,\sigma)$

(a) $P(X>169)=P(z>\dfrac{169-165}{10/\sqrt{25}})=P(z>2)=1-P(z\le2)$

$=1-0.97725=0.02275$

(b) $P(X<163)=P(z<\dfrac{163-165}{10/\sqrt{25}})=P(z<-1)=0.15866$