Question

Question content area top Part 1 Assume that a procedure yields a binomial distribution with n = 5 trials and a probability of success of p = 0.20. Use a binomial probability table to find the probability that the number of successes x is exactly 3. LOADING... Click on the icon to view the binomial probabilities table. Question content area bottom p(3)= enter your response here ​(Round to three decimal places as​ needed.

Answer 1

To find the probability of getting exactly 3 successes in 5 trials with a success probability of 0.20, you use the binomial distribution formula, resulting in a probability of 0.051 after rounding.

Step-by-step explanation:

The subject of this question is a binomial experiment in which we are asked to find the probability of exactly 3 successes in 5 trials, given a success probability of 0.20 per trial. Using the properties of a binomial distribution, we can denote the random variable X = the number of successes. The probability of exactly x successes in n trials is given by P(X = x) = (n choose x) * p^x * q^(n - x), where 'p' is the probability of success, 'q' is the probability of failure (q = 1 - p), and 'n choose x' is the binomial coefficient.

To calculate P(X = 3) where n = 5 and p = 0.20, we use the formula to get P(X = 3) = (5 choose 3) * (0.20)^3 * (0.80)^(5 - 3). This results in P(X = 3) = 10 * (0.008) * (0.64), which simplifies to P(X = 3) = 0.0512. Therefore, the probability that the number of successes x is exactly 3 is 0.051, after rounding to three decimal places as needed.