My answers below

1) A

2) C

3) C (I think we are missing pessimistic days estimation in this question but if not then I would guess B as  3 std deviation can give you 12 day range)

Q1: ANS (A)

1000/500,000 = 0.002 or 0.2% defects per unit, it seems like within a quality goal beacuse 3 sigma is 99.73%

Six sigma is 99.99% it should be close to 50 i believe. Therefore answer is A. (Not sure the answer and calculation though).

Q2: ANS (C)

By utilizing PERT and standard deviaition formulas P+4*MP+O/6 and P-O/6 , we can calculate the following

PERT Calc = 15.667 or 15.67 and SD = 1 or +/- 1, therefore option c should be correct.

Q3: ANS (A)

Range: 23days  - 35 days = 12 days (mean value = 29days)

Pessimistic value is missing here but based on given st, dev. SD=3 at 68.26% means +3 to -3 days 

therefore range = 6 or we can say 26 - 32 days with one standard dev,

hence for two stand. deviation sd = 3x 2 = 6 or +/- 6 range 

so, there is a 95.44% chance that activity will be finished between the 23days - 35days, the answer should be "A" not "C" - calculated based on the value 3 for SD.

Dear Mr. Karthik

This question is manipulated,

1. In first question, questioner is asking 2 questions-  1st is for 3sigma and then for 6sigma.

           As per Normal distribution and 6 sigma theory - this question can be answered like this-

          3sigma - accuracy required - 99.73%  and for 500000 samples defective pieces should not be more     than     0.27% =1350.

Hence if 1000 defective pieces are there, then process is meeting to the 3 sigma accuracy.

6sigma - acuracy required - 99.9996% and for 1million not more than 3.4defects are be there. (0.00034%) hence for 500,000 defects should not be more than  = 1.7~ 2. Means not more than 2 pieces should be defective to meet 6sigma accuracy.

when we go for options - all are vague.

2.   Question 2, is ok answer is C,  the mean value will (12+4x16+18)/6  = 15.7, and sd  =(18-12)/6 = 1

hence for 1sigma  = 68.26 % chance are there for 14.7 to 16.7 days is correct.

Here little confusion may arise with = most likely or realstic chance of duration is 16 days may be considered as mean(myu). But mean value  after calculation by 3 point formula is correct. Most likely value is raw data.

3.

let see:

OP = 18

SD = 3

Most likely is 30

what is chance of 23 to 35 days

now SD =( ps-op)/6 = (ps -18)/6 = 3

hence ps = 36days

Now mean (expected duration) value is  = (18+4x30+36)/6 = 29days

from this value - 23 days  have -6 days variance,

while 35 days have  +6days variance

It ranges between  - 6/3 = - 2sigma to +6/3 = 2sigma

as per this information answer would be  = 95.44%- Option A

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Friends,

I like this forum, but  I  could come very rare here, because of my busy schedule.

Regards