The monthly salaries of workers in a certain factory are normally distributed. The mean salary is ₹4000 and standard deviation is 450. If ₹668 workers are getting salary less than ₹3325, find the total number of workers in the factory.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10,000
Let the total number of workers in the factory be $n$.
Given $μ = 4000, σ = 450$, then $Z =\frac{X-4000}{450}$.
$P(X < 3325) = P\left(Z<\frac{3325-4000}{450}\right)$
$= P(Z<-1.5)= F(-1.5)=1-F(1.5)$
$= 1-0.9332 = 0.0668$
According to given, $0.0668 × n = 668$
$⇒n =\frac{668}{0.0668}=\frac{668}{668}× 10000 =10000$
Hence, total number of workers is 10000.