Answer to Question #323986 in Statistics and Probability for trixie

Question

scores on acommon final examination in alarge enrollment, multiple selection freshman course are normally distributed with a mean of 72. 7 and standard deviation of 13.1 a. Find the probability that the score X on a randomkly selected examination paper is between 70 and 80

Answer 1

We have a normal distribution, $\mu=72.7, \sigma=13.1.$

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

$z_1=\cfrac{70-72.7}{13.1}=-0.21, \\z_2=\cfrac{80-72.7}{13.1}=0.56,$

$P(70<X<80)=P(-0.21<Z<0.56)=\\=P(Z<0.56)-P(Z<-0.21)=$

$=0.71226-0.41683=0.29543$ ​(from z-table).