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?

Answer 1

$P(\bar X>169)=P(Z>\frac{169-165}{\frac{10}{\sqrt{25}}})=P(Z>2)=1-P(Z<2)=0.0228.$