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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?
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Solution
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
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