Question

Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and standard deviation of 100 labour days. if the company promises to construct the flyover in 450 days or less and agrees to pay a penalty of rs. 10,000 for each labour day spent in excess of 450, what is the probability that:

the company pays a penalty of at least rs. 2, 00,000?

Answer 1

To find the probability that the company pays a penalty of at least rs. 2,00,000, we need to calculate the probability that the construction time exceeds 450 days.

Step-by-step explanation:

To find the probability that the company pays a penalty of at least rs. 2,00,000, we need to calculate the probability that the construction time exceeds 450 days.

First, let's standardize the value of 450 with the mean and standard deviation given. Z = (X - μ) / σ

Substituting the values, Z = (450 - 400) / 100 = 0.5

Next, we need to find the cumulative probability for the standardized value using a standard normal distribution table. The cumulative probability for a Z-score of 0.5 is approximately 0.6915.

Therefore, the probability that the company pays a penalty of at least rs. 2,00,000 is approximately 0.6915.