Question

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. 0.20 b. 0.15 c. 0.85 d. 0.411

Answer 1

Solution

Given that ,

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= (₂₀ C ₀) * 0.20⁰ * (0.80)²⁰ + (₂₀ C ₁) * 0.20¹ * (0.80)¹⁹ + (₂₀ C ₂) * 0.20² * (0.80)¹⁸

= 0.411

Probability = 0.411

d)