Final answer:
To find the probability P(X=7) given that X is a binomial random variable with n=25 and p=0.5, we can use the binomial probability formula.
Step-by-step explanation:
To find the probability P(X=7) given that X is a binomial random variable with n=25 and p=0.5, we need to use the formula for the binomial probability:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where C(n, k) represents the binomial coefficient, which is the number of ways to choose k successes out of n trials.
In this case, we want to find P(X=7), so substituting the values into the formula:
P(X=7) = C(25, 7) * (0.5)^7 * (1-0.5)^(25-7)
Using a calculator or software to calculate the binomial coefficient:
P(X=7) = 0.0874