Question

Internet service providers​ (isp) need to resolve customer problems as quickly as possible. for one​ isp, past data indicates that the likelihood is 0.80 that customer calls regarding internet service interruptions are resolved within one hour. out of the next 10 customer calls about interrupted​ service, what is the probability that exactly 7 will be resolved within one​ hour?

Answer 1

I think that the likelihood will still be 0.8 as that means that 8 out of 10 calls will be resolved within one hour so the 7 out of 10 falls within that likelihood so therefore the callers can go by that assumption and be fairly confident that they have quite a high likelihood of having their problems resolved within one hour.

Answer 2

To solve this problem, we make use of the binomial probability formula. That is:

P = [n! / (n – r)! r!] p^r * q^(n – r)

where,

n is the total number of customer calls = 10

r is the number of resolved customer calls = 7

p is the probability of resolving in one hour = 0.80

q is 1 – p = 0.20

Therefore,

P = [10! / (10 – 7)! 7!] 0.80^7 * 0.20^(10 – 7)

P = 0.2013 = 20.13%