question on probability

Submitted by vijayavadrevu on Wed, 04/24/2013 - 18:02

 Regression testing has optimistic estimate of 6days, pessimistic estimate of 36 days, and most likely of 21 days. Calculate probability that regression testing to be completed in 2 - 3 weeks

A)0.526

B)0.998

c)0.682

D)0.956

Answer is given as C

Can some one explain?

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crushPMP

Wed, 04/24/2013 - 18:37

 PERT = (6+36+21*4)/6 = 21 = 3 weeks

2 weeks is 1 standard deviation away = 1 - (3-2)/3 = 66.666%

Ans C is the closest

 

sspawar

Thu, 04/25/2013 - 05:03

This question can be solved like this:

O = 6

P = 36

M = 21

Expexted(Mean ) = 21 (by pert formula (6+4*24+36)/6)

SD  = (P - O)/ 6 = [(36 - 6) /6]  =5 DAYS

3 WEEKS = 21 DAYS = MEAN ----- PROBABILITY of completing job in 3 weeks  will be at Mean , = 50%

2 WEEKS =  14 DAYS  ~  - 1SD (21-14 ~ 5) from mean ----- PROBABILITY of completing in 2 weeks will be  =[50 -( 68.26/2)]%

= 50 -34.13 = 15.87%

because +/- 1SD = 68.26%

hence PROBABILITY OF COMPLETING JOB IN 2-3 WEEKS will be  = 50 -15.87 = 34.13 % or 0.3413

Hence no one option is correct here.

 it is half of the 0.6826

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

exact of 21-14 = 7 days will be (7/5)SD = - 1.4SD, EQUIVALENT PROBABILITY OF -1.4SD WILL BE (from standard probabity chart = 0.4192 (Refer blog post dated 30th May at  er-sspawar.blogspot.in

hence exact probability of 2-3 weeks will be  = 0.5-.4192 = 0.0808

bkthakkar

Thu, 04/25/2013 - 06:00

Agree, Completely with you


Explanation was truly amazing


 

sspawar

Thu, 04/25/2013 - 06:32

 


                                       
                 

 

                  
               

 

 

  

 

                
   

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41.92% PROB

 

    

 

                

 

  
 

 

 

 

 

 

 

    

 

                    

 

 

 

 

 

 

 

 

MEAN

 

 

 

 

 

 

 

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8.08
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3week

            
                                       

 

san

Thu, 04/25/2013 - 07:38

Thank you for the detailed explanation. I understood the second part but the chart will not be available in the exam.

So, I am trying to understand first solution.

I am cleared till PROBABILITY of completing job in 3 weeks 

I am not understanding as how you arrived PROBABILITY of completing job in 2 weeks 

It is mentioned that 1SD (21-14 ~ 5) from mean
that means 50- 7/5(34.13)

But 7/5 value is ignored here.

Please clarify on this point

falcios

Thu, 08/08/2013 - 11:51

Great charts!

Is 41.92% right because that's what I got. It's not one of the answers listed.

The answer is calculating -/+ 1 sd 68%

sspawar

Thu, 04/25/2013 - 09:03

 I am sure in exam , such question which requires any references or itself are lengthy, could not be asked.

it is just for understanding the concepts.

I am also sure that this question is not correct.

hence an approximation upto the known values is taken by me.

 --------------------------

your doubt 

it is corresponding value

for

1sd = area any side of mean = 34.13%

in figure you can imagine 14 days (2 weeks) is 7 days behind of 21 days (mean)

where 5 days = 1sd 

it is by approximation considered that 7 ~5 = 1sd (because generally we know = 1sd = 34.13% and we dont know what is corresponding area of 7 (1.4sd) exactly . 

and hence by chart in second  case, it is shown.

san

Thu, 04/25/2013 - 11:54

Thank you for the explanation..