Question

In an intelligence test conducted on 1000 students, the average scores was 42 and standard deviation 24. 

Find the number of successful students if the minimum pass marks is 40.

Answer 1

Let $X=$ the student's mark: $X\sim N(\mu, \sigma^2)$

Given $\mu=42, \sigma=24$

$$P(X\geq40)=1-P(X<40)$$

$$=1-P(Z<\dfrac{40-42}{24})\approx1-P(Z<-0.083333)$$

$$\approx1-0.4668=0.5332$$

$$0.5332\cdot1000=533$$

The number of successful students is 533.