Answer to Question #169925 in Statistics and Probability for Sheng

Question

The average public high school has 468 students with a standard deviation of 87.If a public school is selected, what is the probability that the number of students enrolled is greater than 400? 

Answer 1

According to distribution function of a normal random variable X with mean = 468 and standard deviation = 87, the probability that number of students enrolled X is greater than 400:

$Pr(X > 400) = 1 - Pr(X \leq 400) =\\=1 - \Phi(\frac{400 - 468}{87}) = 0.7823,$

where $\Phi(x)$ is distribution function of a normal random variable with mean = 0 and standard deviation = 1

So, the probability that the number of students enrolled is greater than 400 is 78%