Question

You conduct 24 Bernoulli trials with probability 0.65 of success. What is the probability that you will obtain exactly 11 or fewer successes? Round your answer to three decimal places. even if the third decimal place is a 0.

Answer 1

This is a binomial distribution.

p = 0.65

n = 24

P(X = x) = 24Cx * 0.65^x * (1 - 0.65)^24-x

P(X < 11) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11)

               = 24C0 * 0.65⁰ * 0.35²⁴ + 24C1 * 0.65¹ * 0.35²³ + 24C2 * 0.65² * 0.35²² + 24C3 * 0.65³ * 0.35²¹ + 24C4 * 0.65⁴ * 0.35²⁰ + 24C5 * 0.65⁵ * 0.35¹⁹ + 24C6 * 0.65⁶ * 0.35¹⁸ + 24C7 * 0.65⁷ * 0.35¹⁷ + 24C8 * 0.65⁸ * 0.35¹⁶ + 24C9 * 0.65⁹ * 0.35¹⁵ + 24C10 * 0.65¹⁰ * 0.35¹⁴ + 24C11 * 0.65¹¹ * 0.35¹³

               = 0.042