Question

Assume that a procedure yields a binomial distribution with a trial repeated

n=5 times. Use some form of technology to find the probability distribution given the probability p=0.156 of success on a single trial.

Answer 1

Explanation:

Use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

n = 5, p = 0.156, and q = 0.844.

r = 0, P = ₅C₀ (0.156)⁰ (0.844)⁵⁻⁰ = 0.428

r = 1, P = ₅C₁ (0.156)¹ (0.844)⁵⁻¹ = 0.396

r = 2, P = ₅C₂ (0.156)² (0.844)⁵⁻² = 0.146

r = 3, P = ₅C₃ (0.156)³ (0.844)⁵⁻³ = 0.027

r = 4, P = ₅C₄ (0.156)⁴ (0.844)⁵⁻⁴ = 0.002

r = 5, P = ₅C₅ (0.156)⁵ (0.844)⁵⁻⁵ ≈ 0