terça-feira, setembro 05, 2006

PMP Question ? - Probability Distributions

I'm not sure this is really necessary for the PMP Exam, but better safe than sorry.

I had to look it up in the book "Introduction to the Theory and Practice of Econometrics" by George G. Judge et al ( ISBN = 0-471-60272-8 ). I've got the 2nd edition of this book. Anyone interested in buying it should get the last edition.

Here it goes.

Binomial Distribution (Success or Failure)

• A coin will be tossed 5 times but the coin is biased so that the probability of heads for each toss is 0.04. Heads is success, tails is failure.
• N = number of items in the sample (the number of coin tosses)
• X = number of items for which the probability is desired (number of Heads)
• In Appendix A we go to column N and find where N = 5
• In Appendix A we go to where p = 0.40
• Each row represents the probability of 0, 1,2, 3, 4, and 5 successes
• Add them up

Poisson Distribution

• A lightbulb manufacturer has a known defective rate of 4%. From a sample of 40, the probability of 4 or more defective light
• µ = np = (40) (.04) = 1.6
• Probability of 4 or more defective is = 1 – probability of 3 or less defective
• In the table, find where µ = 1.6
• Add up the numbers where x has a value of 0, 1, 2, or 3 (this is the P of 3 or less defectives)
• Subtract that number from 1.0
• Find np (sample x defective rate)
• Calculate up to by going to the table, finding np, adding it up
• Subtract that answer from 1 to x or greater probability

Normal Distribution (also known as Gaussian)

• If process produces parts with mean of _ and standard Deviation of _, what is the P that one random part has a measurement of _?
• Mean time of a bank transaction is 5.25 with a standard deviation of 0.75 minutes and the values are normally distributed. What is the probability that a transaction will occur between 4.0 and 5.25 minutes and below 4.0?
• Z = 4.0 – 5.25/ 0.75 = -1.67
• Go to Appendix A and find 1.67 = 0.4525
• Because we know that µ is 5.25, the probability that a transaction will take less than 5.25 is .05 (1/2)
• Therefore, the probability that a transaction will be less than 4 minutes = 0.5 – 0.4525 = 0.0475

Sampling Distributions (number of standard Deviations that a sample mean is away from the population mean)

• If normal distribution with mean of _ and SD of _. From sample of _ what is P that the sample mean is >, <, =, or between _?
• Hospital emergency room where it has a record waiting time of 30 minutes with a standard deviation of 5 minutes. If a sample of 35 is measured, what is the probability that the sample mean would be greater than 31.5 minutes?
• Do the Z calculation to get 1.77
• Find 1.77 in Appendix A (go to 1.7 and then across to 0.07)
• Subtract that probability from the .5 probability = .50 - .4616 = .0384
• This tells us that there is only a .0384 probability that, from the sample of 35, the sample mean will be greater than 31.5.

I hope it will help ...

NB : The appendix A referred in the notes contains all the tables that allow the calculation of the probabilities. On this day and age, I always use the scientific calculator ...

2 comentários:

Abbey Ray disse...
Este comentário foi removido pelo autor.
Abbey Ray disse...

"Hi There,

Very Nice post on PMP uestions.That was very helpfull.keep posting"