Answer to Question #327785 in Statistics and Probability for RAIZO

Question

500 children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that a child, picked at random has a height greater than 120 cm?

Answer 1

We have a normal distribution, $\mu=110, \sigma=6.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{120-110}{6}=1.67.$

$P(X>120)=1-P(X<120)=\\= 1-P(Z<1.67)=\\ =1-0.9525=0.0475 \text{ (from z-table).}$