Question

CAT Construction has been awarded a contract with the City of Newberg to replace and repair all of the sidewalks in the older residential areas. Based on experience with previous​ projects, CAT feels the project completion time follows a normal distribution with a mean of 60 days and a standard deviation of 10 days.

CAT anticipates the net profit for completing the project is​ $100,000.

If the company completes the project is less than 40​ days, it will receive an additional​ $25,000 bonus.

If the company takes longer than 75 days to complete the​ project, the City will penalize CAT​ $20,000.

Use the 4 decimal probabilities when using the​ z-tables.

​CAT's expected profit on the project​ is:

A.​$100,000

B.​$101,214

C.​$99,234

D.​$90,274

Answer 1

Solution: The correct option is:

C. $99,234

Explanation:

The amount of $100,000 is certain for the company if they complete the project.

We are given that if the company completes the project is less than 40​ days, it will receive an additional​ $25,000 bonus.

The z-score for the number of days less than 40 is:

Using the standard normal table, we have:

Therefore, the expected bonus amount if the project is completed in less than 40 days is:

We are also given that if the company takes longer than 75 days to complete the​project, the City will penalize CAT​ $20,000.

The z-score for the number of days greater than 75 is:

Using the standard normal table, we have:

Therefore, the expected penalty amount if the project is completed in greater than 75 days is:

Therefore, the ​CAT's expected profit on the project​ is​CAT's expected profit on the project​ is: