Answer to Question #300987 in Statistics and Probability for Roanne

Question

In a Math test, the mean score is 45 and the standard deviation is 4.

Assuming normality, what is the probability that a score picked at random will lie

c. between 35 and 53?

Answer 1

$\mu=45\\\sigma=4$

Let the random variable $X$ represent the math score.

$p(35 \lt x\lt53)=p({35-45\over4}\lt Z\lt {53-45\over4})=p(-2.5\lt Z\lt 2)=\phi(2)-\phi(-2.5)=0.9772-0.0062=0.991$

The probability that a score picked at random will lie between 35 and 53 is 0.991