Answer to Question #323638 in Statistics and Probability for Toilet Gamer

Question

The heights of male are normally distributed with mean of 170 cm and standard deviation of 7.5cm. Find the probability that a randomly selected male has a height > 180 cm.

Answer 1

We have a normal distribution, $\mu=170, \sigma=7.5.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{180-170}{7.5}=1.33;$

$P(X>180)=P(Z>1. 33)=\\=1-P(Z<1.33)=$

$=1-0.9082=0.0918$ ​(from z-table).