Answer to Question #304122 in Statistics and Probability for Tupa

Question

The height of learners (in cm) at a high school can be described by the N(174.50,47.61) distribution. If 1000 learners are randomly selected from the school, how many of them would you expect to have a height of less than 160.0 cm?

Answer 1

This is a normal distribution with $\mu=174.50,\;\sigma=\sqrt{47.61}=6.9.$

$P(X<160.0)=P(Z<\frac{160-174.50}{6.9})=P(Z<-2.10)=0.0178.$

Number of persons: $n=0.0178*1000=18.$