Question

The distribution of scores on the SAT is approximately normal with a mean of 500 and a standard deviation of 100. For the population of students who have taken the SAT, what proportion have a sat score less than 400?

Answer 1

`\mathbb P(X<400)=\mathbb P\left((X-500)/(100)<(400-500)/(100)\right)=\mathbb P(Z<-1)\approx0.1587`