Question

Let X be a random variable that follows a binomial distribution with n=12, and probability of success ( p=0.81 ) Determine: P(X=10) ? 0.251111 0.695706 0.304294 0.289669

Answer 1

To find P(X=10) for a binomial distribution with n=12 and p=0.81, use the binomial formula. Calculate '12 choose 10', raise the success probability to the 10th power, and the failure probability to the 2nd power, then multiply these values together. The closest match to the calculated result is the correct probability. Upon completing these calculations, P(X=10) is closest to one of the given options, which should be selected as the final answer.

Step-by-step explanation:

To determine the probability that a random variable X, which follows a binomial distribution with n=12 and p=0.81, is exactly 10 (P(X=10)), you use the binomial probability formula:

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

Let's calculate it step by step:

1. First, we determine n choose x, which is the number of ways we can choose 10 successes out of 12 trials. This is calculated as 12 choose 10 or (12!)/(10!*(12-10)!).
2. Next, we raise the probability of success (p) to the power of x, which is 0.81^10.
3. Then, we raise the probability of failure (q=1-p) to the power of n-x, which is (1-0.81)^2.
4. Finally, we multiply all these values together to get P(X=10).

Upon completing these calculations, P(X=10) is closest to one of the given options, which should be selected as the final answer.