The marks obtained in a certain examination follow normal distribution with mean 30 and standard deviation 10. If 1000 students appeared in the examinations, calculate the number of students scoring more than 50 marks.

23

The correct answer is Option (2) → 23

Let X denote the marks obtained in the examination.

Given $μ = 30, σ = 10$, then $Z =\frac{X-30}{10}$

$P(X >50) = P\left(Z >\frac{50-30}{10}\right)= P(Z > 2)$

$= 1-P(Z≤2) = 1- F(2) = 1-0.9772$

$= 0.0228$

∴ Number of students scoring more than 50 marks

= 1000 × 0.0228 = 22.8 i.e. 23.

Hence, 23 students scored more than 50 marks.