Question

In a binomial distribution with n = 10 and p = 0.15, find the probabilities of the following events:

a. P(x = 2)
(A) 0.250
(B) 0.086
(C) 0.179
(D) 0.323

b. P(x ≤ 2)
(A) 0.179
(B) 0.572
(C) 0.250
(D) 0.907

Answer 1

To find the probabilities in a binomial distribution with n = 10 and p = 0.15, P(x = 2) is 0.086 and P(x ≤ 2) is 0.179.

Step-by-step explanation:

To find the probabilities in a binomial distribution with n = 10 and p = 0.15:

a. P(x = 2):

This represents the probability of getting exactly 2 successes in 10 trials. We can calculate this using the binomial probability formula:

P(x = 2) = C(10, 2) * (0.15)^2 * (1-0.15)^(10-2) = 0.086

So the answer is (B) 0.086.

b. P(x ≤ 2):

This represents the probability of getting 2 or fewer successes in 10 trials. We can calculate this using the cumulative binomial probability formula:

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2) = C(10, 0) * (0.15)^0 * (1-0.15)^(10-0) + C(10, 1) * (0.15)^1 * (1-0.15)^(10-1) + C(10, 2) * (0.15)^2 * (1-0.15)^(10-2) = 0.179

So the answer is (C) 0.179.