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 less than 45 kg.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.0062
Let X denote the weight of the students of class XII.
Given $μ = 50, σ = 2$, then $Z =\frac{X-50}{2}$
$P(X <45) = P\left(Z <\frac{45-50}{2}\right)= P(Z<-2.5)$
$= F(-2.5)=1-F(2.5) = 1-0.9938$
$= 0.0062$