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?
A)0.85
B)0.15
C)0.20
D)0.411

Question

Quizplus · Accepted Answer

The probability of success (a cable customer switching) is 20% or 0.2, and the probability of failure (a cable customer not switching) is 80% or 0.8. Therefore, using the binomial probability formula: P(X ≤ 3) = Σ(20 choose k) (0.2)^k (0.8)^(20-k) for k = 0, 1, 2, 3. Calculating this sum gives P(X ≤ 3) = 0.4108 or approximately 0.411. Therefore, the probability that no more than 3 customers would be willing to switch their cable is 0.411.

Historical Data Indicates That Only 20% of Cable Customers Are