Answer to Question #311821 in Statistics and Probability for asasas

Question

The ages of participants in a drama workshop are normally distributed with mean 18.5 years and standard deviation 2.5 years. What is the probability that the age of a random participant is (a) more than 20 years, (b) between 16 and 18 years?

Answer 1

We have a normal distribution, $\mu=18.5, \sigma=2.5.$

Let's convert it to the standard normal distribution, $z=\cfrac{x-\mu}{\sigma}.$

(a) $z=\cfrac{20-18.5}{2.5} =0.6;$

$P(X>20)=P(Z>0.6)=1-P(Z<0.6)=$

$=1-0.7257=0.2743$   (from z-table).

(b) $z_1=\cfrac{16-18.5}{2.5}=-1, z_2=\cfrac{18-18.5}{2.5}=-0.2,$

$P(16<X<18)=P(-1<Z<-0.2)=P(Z<-0.2)-P(Z<-1)=$

$=0.4207-0.1587=0.2620$ (from z-table).