Problem 3

Bidding Simulation using variables with uniform and normal distributions

As a building contractor, you are preparing a bid on a new construction project. Three other contractors will be submitting bids for the same project. Based on past bidding practices, bids from the other contractors can be described by the following probability distributions:

Contractor A - Uniform probability distribution between $660,000 and $850,000

Contractor B - Normal probability distribution with a mean bid of $740,000 and a standard deviation of $40,000

Contractor C - Normal probability distribution with a mean bid of $760,000 and a standard deviation of $20,000

Remember that of the 4 contractors (you, Contractor A, Contractor B, and Contractor C), the contractor with the lowest bid wins the contract!

(A) If you submit a bid of $720,000, what is the probability that you will win the contract when you use 1,000 trials to simulate the bidding process? __________% (record what you calculate, though I understand it will change as you make changes in the worksheet)

(B) Attach a table that displays the first 4 trials and the last 4 trials (hiding all rows in between) and depicts your probability of winning. Give appropriate units to each variable (e.g., currency when in dollars). Make an area on the worksheet where you display formula for each formula used in the trials and all formulas involved in calculating the probability of winning. [You can accomplish this by cutting and pasting your formula but putting an apostrophe ahead of it to display as a text string. For example, the formula =average(B2:B10) can be displayed by writing it in a cell as '=average(B2:B10).]

(C) You are now considering the consequences of different bids. What happens to your probability of winning the contract if you lower your bid to $680,000? ________________

(D) What happens to the probability of winning the contract if you increase your bid to $820,000? _____________

[Note: Remember that your answers will differ based on the random numbers generated in your simulation.]