Probability Distribution

Submitted by kmkan28 on Sun, 03/03/2013 - 14:24

Hi,

This is a question i have taken from a question bank.Please give me answer and the explanation.

 

The cost estimatesof a proposed project has an expected value of 1000000 and a standard deviation of 50000.The project is budgeted for 1100000 so as to include a contingency reserve.Assuming that the cost estimates are normally distributed,what is the probability of completing this project over budget?

A.0.1
B.0.05
C.0.025
D.05

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sspawar

Sun, 03/03/2013 - 16:25

 C

kmkan28

Sun, 03/03/2013 - 16:39

Dear pawar!,

This is the answer given in the portal also.But we need your explanation.

 

sspawar

Sun, 03/03/2013 - 17:22

Question 

is asking that what is probability that work completion amount may ecceed the BAC.

you know contingency reserve is part of baseline / BAC.

Expected value ( Mean) = 1000000

SD = 50000

BAC = 1100000 = 1000000 + (2*50000) = MEAN + 2SD

With this amount Probability  of work completion under budget or on budget is =  50% + (95/2)%

= 97.5 %

or = 0.975

Probability that work completion amount may ecceed the BAC (1100000) = 1-0.975 = 0.025

pradipchavan82

Mon, 03/04/2013 - 18:44

SSPAWAR, Thanks for your explanation. My question to you is why did we choose 2SD in your explanation.

Can;t it it be 1SD? 

sspawar

Tue, 03/05/2013 - 04:54

 Bks contingency amount is 100000 above expected value (mean)  and it is equivelant of = 2*50000 = 2sigma = 2SD.

Here dont confuse with 2sd = +/- 1sd either side of mean, 100000 (2sigma) is completely right side of mean value (1000000).

kmkan28

Tue, 03/05/2013 - 14:36

Pawar,

I just wanted to ask the same question.Great reply.

 

Mani

amar

Thu, 03/07/2013 - 19:45

Hi sspawar,

I didn't get the :

work completion under budget or on budget is =  50% + (95/2)%

Which formula is this. I understand 95 refers to 2SD..please explain.

Thanks.

sspawar

Fri, 03/08/2013 - 02:25

68.26 % is for +/-1SD

95.45% is for +/- 2SD

99.73 % is for  +/-3SD

99.9996% is for +/-6SD

------------------------------------

68.26 = 34.13 % left side of Mean (Middle pick) equivelant to  (-1SD), and 34.13 %right side of Mean (Middle pick) equivelant to  (+1SD), 

like wise 

95 = 4sd and 95/2 = 2sd

amar

Fri, 03/08/2013 - 05:02

 I am still trying to understand this. I am sure I need more time. Not sure exactly how the 50% came in the calculation.

Thanks.

sspawar

Fri, 03/08/2013 - 08:02

It is supposed  that Complete area below bell shape curve = 1 unit = 100%

Left side of Mean (middle pick) will be half of this = 0.50unit = 50%

Right side of Mean (middle pick) will be half of this = 0.50unit = 50%

Now it is also fixed that 

Left side of 34.13% area have a fixed distance from mean = one SD, though it is LHS of mean hence called -1SD

Right side of 34.13% area have a fixed distance from mean = one SD, though it is RHS of mean hence called +1SD

Adding both 68.26% equally spreaded both side of mean will have  = +1SD and -1SD distance  = +/- 1 SD = inactual this distance will be 2SD

Like for Area 99.73% (49.87% +49.87),  +/- 3SD = 3SD left +3SD right = 6SD distance

See both figure of dated 29May12 in blog

er-sspawar.blogspot.in

bkthakkar

Sat, 03/09/2013 - 02:19

Great answer.. strong fundamentals

 

sspawar

Fri, 03/08/2013 - 08:27

Normal Distribution

 

Data can be "distributed" (spread out) in different ways.

It can be spread out more on the left ... or more on the right

Or it can be all jumbled up

 

But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this:

 

A Normal Distribution

The "Bell Curve" is a Normal Distribution.
And the yellow histogram shows some data that follows it closely, but not perfectly (which is usual).

It is often called a "Bell Curve"
because it looks like a bell.

sspawar

Fri, 03/08/2013 - 09:07

In More Detail

Here is the Standard Normal Distribution with percentages for every half of a standard deviation, and cumulative percentages:

Example: Your score in a recent test was 0.5 standard deviations above the average, how many people scored lower than you did?

  • Between 0 and 0.5 is 19.1%
  • Less than 0 is 50% (left half of the curve)

So the total less than you is:

50% + 19.1% = 69.1%

In theory 69.1% scored less than you did (but with real data the percentage may be different)

amar

Fri, 03/08/2013 - 16:10

This really helped me. It's better to remember this concept and apply if it ever appear. But hard to think such complex question will appear in exam. You must be an expert in statistics as well. Thanks for explaining sir.