Question

Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company pay a penalty of at least ₹ 2,00,000?

Answer 1

Let x be a normal variate with mean 400 labour days and standard deviation of 100 labour days

m = 400 and σ = 100

The construction work should be completed within 450 days.

The standard normal variate

= `(x - mu)/6 = (x - 400)/100`

Personality for 1 labour day = ₹ 10,000

If personality amount is = 2,00,000 than No of excess

Days = `200000/10000` = 20

∴ x = 450 + 20 = 470

When x = 470

z = `(470 - 400)/100 = 70/100` = 0.7

= P(X ≥ 470) = P(Z ≥ 0.7)

= 0.5 – 0.2580

= 0.2420