Answer to Question #325704 in Statistics and Probability for Chang

Question

Determine the area of the normal distribution with mean of 10, standard deviation of 5 and scores between 5 to 12

Answer 1

We have a normal distribution, $\mu=10, \sigma=5.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}.$

$z_1=\cfrac{5-10}{5}=-1;\\ z_2=\cfrac{12-10}{5}=0.4;\\ P(5<X<12)=P(-1<Z<0.4)=\\ =P(Z<0.4)-P(Z<-1)=\\ =0.6554-0.1587=0.4967 \text{ (from z-table).}$