Koshila D.

asked • 08/01/15

In binomial distribution rule, what is the value of p ? Is it 0.15 or 0.75(15%*5)

A machine produces 15% defective items.In a sample of 5, drawn at random, using binomial distributuion,Find the probabilities that :

a) there'll be 4 defective items
b) there will not be more than 3 defective items
c) all will be non defective

1 Expert Answer


Nicholas J. answered • 08/01/15

New to Wyzant

Duke University PhD; Math, Comp Sci, Econ; 10+ Years Experience

Koshila D.

Yeah thanks a lot. I got it clear now.
But the question in my mind is that machine produces 15% defective items, so for 5 items isn't it (15% x 5...???


Nicholas J.

The key here is that p represents the probability of success of failure on Each individual trial.
There are n=5 trials, each with probability p = 0.15 of being defective.
I think maybe you are confusing p with the average number of defective items that would be produced in a sample of 5 items, this is also sometimes referred to as the 'expectation' of the binomial distribution.
  The formula for the expectation of a binomial distribution is n*p
  Or in this case, the expected number of defective items is 5*0.15 = 0.75


Nicholas J.

Another interesting thing to point out is that the expectation n*p is not necessarily less than or equal to 1.
p is the probability of a 'success' on each trial,
Because p is a probability, we know that p must be less than or equal to 1.
For example, if we were looking at a sample of size 50, instead a sample of size 5, then
  n*p = 50*0.15 = 7.5
  but we can't set p = 7.5, because then p wouldn't be a valid probability


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