10,000 students take a test whose marks are normal with mean 50 and standard deviation 10. About how many score below 40? (Take $P(0 < Z < 1) = 0.3413$.)

Explanation

1. 01

   $z = \frac{40 - 50}{10} = -1$, and $P(Z < -1) = 0.5 - 0.3413 = 0.1587$.

2. 02

   $0.1587 \times 10{,}000 = 1{,}587$ students.