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January 30, 2015

January 30, 2015

Posted by **Camela** on Wednesday, December 26, 2012 at 9:14pm.

- statistics -
**MathMate**, Wednesday, December 26, 2012 at 9:45pmRecall that if the following conditions are met, we can use a binomial distribution to model the situation:

1. there are only two possible outcomes (operating or not operating, i.e. a bernoulli experiment)

2. probability applies to all units observed, and does not change.

3. random events

If we use the binomial distribution, where p=0.7 (success) and q=0.3 (failure) then the probability of success of i batteries out of n=50 are given by:

nCi*p^i*q^(n-i)

where nCi = n!/((n-i)!i!)

So calculate the probabilities for i=20,21,22,23,24,25 and sum them to get the probability that 20-25 batteries will remain operational.

I get about 0.0024

- statistics -
**MathMate**, Wednesday, December 26, 2012 at 9:47pmSorry, it should be for 25-30 operating batteries, I get about P(25-30)=0.084

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