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 takes at most 500 days to complete the flyover?

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

P(at most 500 days) = P(X ≤ 500 )

When x = 500

z = `(500  - 400)/100 = 100/100` = 1

P(X ≤ 500) = P(Z ≤ 1)

=P(`∞` < z < 0) – r – P(0 < z < 1)

= 0.5 + 0.3415

= 0.8413