Answer to Question #281842 in Statistics and Probability for Sam

Question

The random variable Y is normally distributed with expectation a=75 and standard deviation equal to 28. Use the Laplace function to find the probability that the test result will be assigned to a random value within the interval [147, 231]

Answer 1

$P(147<Y<231)=P(147<N(75,28^2)<231)=P(147<75+28N(0,1)<231)=P(2.57<N(0,1)<5.57)=F(5.57)-F(2.57)\approx0.5-0.4949=0.0051$

F(x) - Laplace function