The weights of students of class XII follow normal distribution with mean 50 kg and standard deviation 2 kg. Find the probability that a student selected at random will have weight between 48 and 56 kg.

0.8399

The correct answer is Option (3) → 0.8399

Let X denote the weight of the students of class XII.

Given $μ = 50, σ = 2$, then $Z =\frac{X-50}{2}$

$P(48 <X <56) = P\left(\frac{48-50}{2} <Z<\frac{56-50}{2}\right)$

$= P(-1<Z<3) = F(3) - F(-1)$

$= F(3)-[1-F(1)] = 0.9986-[1-0.8413]$

$= 0.9986-0.1587=0.8399$