Question

The Grade 11 students of Capiz National High School took a 100 item Statistics exam. The scores fit the normal distribution with a mean of 75 and a standard deviation of 10. What is the percentage of students that got a score of 80 to 85?

Answer 1

We have a normal distribution, $\mu=75, \sigma=10.$

Let's convert it to the standard normal distribution,

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

$z_1=\cfrac{80-75}{10}=0.5;\\ z_2=\cfrac{85-75}{10}=1;\\ P(80<X<85)=P(0.5<Z<1)=\\ =P(Z<1)-P(Z<0.5)=\\ =0.8413-0.6915=\\ =0.1498=14.98\% \\ \text{ (from z-table).}$