SOLUTION: 1-Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the

Question 1094890: 1-Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that no more than 3 customers would be willing to switch their cable?
Answer 0.85 0.15 0.20 0.411 0.589
I know the answer is .411 but have no idea how I got there.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

This is a straightforward application of the binomial formula. If the probability is .2 that each customer is willing to switch and .8 that they are not, then the probability that n of the 20 customers will be willing to switch is

where "C(20,n)" is "20 choose n".

Since you want the probability that no more than 3 of the 20 customers will be willing to change plans, the calculations you need to perform are...

[0 willing to switch];
[1 willing to switch];
[2 willing to switch]; and
[3 willing to switch]

Then of course you need to add the probabilities for those 4 cases.

The calculations are tedious with pencil and paper, and even with a scientific calculator; a spread sheet works nicely.

And .411 is the right answer....

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