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.
Answer & explanation
Correct answer: option 2
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.