A building contractor is preparing a bid on a new construction project. Two othe

Question

A building contractor is preparing a bid on a new construction project. Two 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:

If required, round your answers to three decimal places.

If the building contractor submits a bid of $670,000, what is the probability that the building contractor will obtain the bid? Use an Excel worksheet to simulate 1,000 trials of the contract bidding process.

The probability of winning the bid of $670,000 = .658

The building contractor is also considering bids of 695,000 and $705,000. If the building contractor would like to bid such that the probability of winning the bid is about 0.5, what bid would you recommend? Repeat the simulation process with bids of $695,000 and $705,000 to justify your recommendation.

The probability of winning the bid of $695,000 = _____
The probability of winning the bid of $705,000 = ______

Contractor Probability Distribution of Bid A Uniform probability distribution between $520,000 and $720,000 B Normal probability distribution with a mean bid of $620,000 and a standard deviation of $42,000

Explanation / Answer

(a) For the bids of 670,000 create 3 columns in excel as A, B, C

Where A and B are the 2 constructors and C is the one for whom we are considering the bid.

To generate simulation consider the following formulas:

in Col. A :" =RAND() * (720000-520000) + 520000 " :this will generate Uniform(520000,720000)

in Col.B :" =NORMINV(RAND(),620000,42000) " :this will generate Normal(620000,42000^2)

in Col. C:" =IF(AND(A2<670000,B2<670000),1,0) " :that will impose double condition on A and B and return if C wins the bid!

Drag it using fil-handle upto 1001 (since 1st row is for variable names)

Then use " =sum(c2:c1001) " this will count total number of 1's.

Then probability of wining the bid is = sum/1000

Here it is =0.65 (that may vary!)

(b)Similarly create 2 more colmns , one for 695000 and other one for 705000

and use the 2 formulas respectively

" =IF(AND(A2<695000,B2<695000),1,0) "

" =IF(AND(A2<705000,B2<705000),1,0) "

Then calculate the sum and divide by 1000 for both the columns

Prob[Winning the bid 695000] = 0.828

Prob[Winning the bid 705000] = 0.892

As bid probability should be around 0.5 , then the recommended bid would be 695,000

Since it is less in value but satisfies the probability criteria of the bidder!

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