Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X≤4), n=6, p=0.8

Answer 1

P(X = x) = nCx * p^x * (1 - p)^n-x

P(X < 4) = 1 - P(X > 4)

              = 1 - (P(X = 5) + P(X = 6))

              = 1 - (6C5 * 0.8⁵ * 0.2¹ + 6C6 * 0.8⁶ * 0.2⁰)

              = 1 - 0.6554

              = 0.3446