Answer to Question #202487 in Statistics and Probability for Leonie Patrocinio

Question

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting between the mean and a score of 50

Answer 1

$z_2=\frac{x_2-\mu}{\sigma}==\frac{80-80}{10}=0$

$z_1=\frac{x_1-\mu}{\sigma}=\frac{50-80}{10}=-3.00$

$P(z<0)=0.5$

$P(z<-3.00)=0.00135$

$P(50<x<80)=P(z<0)-P(z<-3.00)=0.5-0.00135=0.49865$