# Standardized Normal Distribution

Let's assume I have a test subject of $n$ students. If I already know the mean and sd values how can I find how many students have a value greater than $y$? For reference let mean = $10$, sd = $5$, $n = 1.000.000$ and $y= 13$.

The way I've approached this question so far is this: \begin{eqnarray} P(X > 13) = 1 - P\left(Z < \frac{13 - 10}{5}\right). ~~~~~~~~~~~~~~~~~~~~~~~~ (1) \end{eqnarray} Thus I got the probability. My real problem is how to use the number of students given to get the result. Should I just multiply the result I got from (1) with $n$ or is there another way of solving this?

• Did you mean $\frac{13-10}{5}$? Commented May 19, 2018 at 21:01
• yeah i did mean that Commented May 19, 2018 at 21:15
• If $x$ is $13$, it is not a random variable. Commented May 19, 2018 at 21:27
• you are right, my mistake Commented May 19, 2018 at 21:33
• If you have 100 students each with a 40% chance of getting an A, on average how many of the 100 do you expect to get A's? Commented May 20, 2018 at 1:42