Assume that a procedure yields a binomial distribution with a trial repeated $n = 30$ times. Use the binomial probability formula to find the probability of $x = 5$ successes given the probability $p = 1 / 5$ of success on a single trial. Round to three decimal places.
A) $0.067$
B) $0.172$
C) $0.198$
D) $0.421$

Question

Quizplus · Accepted Answer

To find the probability of exactly 5 successes in 30 trials with a probability of success of 1/5 on a single trial, we plug in the values into the binomial probability formula:

P(x = 5) = (30 choose 5) * (1/5)^5 * (4/5)^25

Using a calculator or software, we get:

P(x = 5) ≈ 0.172

Therefore, the best choice is B.

Assume That a Procedure Yields a Binomial Distribution with a Trial