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

Algebra ->  Probability-and-statistics -> 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       Log On


   

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) About Me  (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
C%2820%2Cn%29%2A%28.8%5En%29%2A%28.2%5E%2820-n%29%29
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...

C%2820%2C0%29%2A%28.8%5E20%29%2A%28.2%5E0%29 [0 willing to switch];
C%2820%2C1%29%2A%28.8%5E19%29%2A%28.2%5E1%29 [1 willing to switch];
C%2820%2C2%29%2A%28.8%5E18%29%2A%28.2%5E2%29 [2 willing to switch]; and
C%2820%2C3%29%2A%28.8%5E17%29%2A%28.2%5E3%29 [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....