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 less than 33 marks.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 618
Let X denote the marks obtained in the examination.
Given $μ = 30, σ = 10$, then $Z =\frac{X-30}{10}$
$P(X <33) = P\left(Z <\frac{33-30}{10}\right)= P(Z < 0.3)$
$= F(0.3) = 0.6179$
∴ Number of students scoring less than 33 marks
= 1000 × 0.6179 = 617.9 i.e. 618.
Hence, 618 students scored less than 33 marks.