Question

An achievement test was administer to a class of 20,000 students. The mean score was 80 and the standard deviation was 11. If Lingard scored 72 in the test, how many students did better than him?

Answer 1

$N=20000 \\ \mu=80 \\ \sigma=11 \\ P(X>72) = 1 -P(X<72) \\ = 1 -P(Z< \frac{72-80}{11}) \\ = 1 -P(Z < -0.7272) \\ = 1 -0.2336 \\ = 0.7664 \\ n(X>72) = 20000 \times 0.7664 = 15328$

Answer: 15328 students were better than Lingard