Answer to Question #341551 in Statistics and Probability for Zephyyy

Question

The Test score for a class are normally distributed . what is the the probability a student scored above 90. Given: µ = 75

Ơ = 10

Answer 1

We have a normal distribution, $\mu=75, \sigma=10,x=90.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{90-75}{10}=1.5; \\P(X>90)=P(Z>1.5)=1-P(Z<1.5)=\\ =1-0.9332=0.0668\text{ (from z-table)}.$