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 between 30 and 45 marks.

433

The correct answer is Option (1) → 433

Let X denote the marks obtained in the examination.

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

$P(30 <X < 45) = P\left(\frac{30-30}{10}<Z<\frac{45-30}{10}\right)$

$= P(0 <Z<1.5) = F(1.5) - F(0)$

$= 0.9332-0.5= 0.4332$

∴ Number of students scoring between 30 and 45 marks

= 1000 × 0.4332 = 433.2 i.e. 433.

Hence, 433 students scored between 30 and 45 marks.