Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X>4)
, n=8
, p=0.7
To find P(X>4), we need to calculate the probability of obtaining 5, 6, 7, or 8 successes in 8 trials.
P(X>4) = P(X=5) + P(X=6) + P(X=7) + P(X=8)
Using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(X=5) = (8 choose 5) * 0.7^5 * 0.3^3 = 0.2362
P(X=6) = (8 choose 6) * 0.7^6 * 0.3^2 = 0.2756
P(X=7) = (8 choose 7) * 0.7^7 * 0.3^1 = 0.2335
P(X=8) = (8 choose 8) * 0.7^8 * 0.3^0 = 0.0824
Adding these probabilities together:
P(X>4) = 0.2362 + 0.2756 + 0.2335 + 0.0824 = 0.8277
Therefore, P(X>4) is approximately 0.8277.