Question

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Suppose that X is a binomial random variable with n = 11 and p = 0.28. Find P 5).
Write only a number as your answer. Round to 4 decimal places (for example
0.1849). Do not write as a percentage.
Your Answer:

Answer 1

Explanation:

To find P(X = 5), we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where n is the number of trials, p is the probability of success on each trial, k is the number of successes we want to find, and (n choose k) is the binomial coefficient, which can be calculated as:

(n choose k) = n! / (k! * (n - k)!)

Plugging in the values n = 11, p = 0.28, and k = 5, we get:

P(X = 5) = (11 choose 5) * 0.28^5 * (1 - 0.28)^(11 - 5)

Using a calculator to evaluate this expression, we get:

P(X = 5) ≈ 0.1397

Therefore, the probability of getting exactly 5 successes in 11 trials, where the probability of success on each trial is 0.28, is approximately 0.1397, rounded to 4 decimal places.