Question

The distribution of monthly income of Rs. 5,000 workers of a factory follows Normal distribution with mean Rs. 10,000 and standard deviation Rs. 1,000. Find the probability of the number of workers. 

(i) having income more than Rs. 9,000 

(ii) having income in between Rs. 8,500 and Rs. 12,000.

Answer 1

Let x be the monthly income is a normal variate with the parameters μ= 10,000 and σ = 1,000 and N = 5000. Then S N.V is

(i) P(income more than Rs. 9000) = P(X > 9000)

No. of workers = 0.8413 × 5000 = 4206.5

(ii) P(income between Rs.8500 and Rs.12,000) = p(8500 < x < 12000)

= Area from (-1.5) to ∞ – Area from 2 to ∞

= 0.9332 – 0.0228 = 0.9104

No. of Workers = 0.9104 × 5000 = 455.2.