Question

In a binomial distribution, n = 4 and π=0.27 . Find the probabilities of the following events. (Round your answers to 4 decimal places.)

a. x = 2.

b. x ≤ 2.

c. x ≥ 3.

Answer 1

Step-by-step explanation:

a. Using the formula for the probability mass function of a binomial distribution:

P(x=2) = (4 choose 2) * (0.27)^2 * (0.73)^2 = 0.3185

b. Using the cumulative distribution function:

P(x ≤ 2) = P(x=0) + P(x=1) + P(x=2) = (4 choose 0) * (0.27)^0 * (0.73)^4 + (4 choose 1) * (0.27)^1 * (0.73)^3 + (4 choose 2) * (0.27)^2 * (0.73)^2 ≈ 0.7575

c. Using the complementary probability:

P(x ≥ 3) = 1 - P(x ≤ 2) = 1 - [(4 choose 0) * (0.27)^0 * (0.73)^4 + (4 choose 1) * (0.27)^1 * (0.73)^3 + (4 choose 2) * (0.27)^2 * (0.73)^2] ≈ 0.2425