Answer to Question #330704 in Statistics and Probability for thin

Question

In a Science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what percent of the score is:

14. Between 30 and 48?

Answer 1

X~$N(42,5^2)$

$P(30<X<48)=P(30<N(42,5^2)<48)=P(30<42+5N(0,1)<48)=P(-2.4<N(0,1)<1.2)=0.88493-0.00820=0.87673$