Question 9 of 10, Step 1 of 1
$7 / 10$
Correct
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.
\[
P(X \leq 4), n=7, p=0.6
\]
Answer
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Step 1 ：The problem is asking for the probability that a binomial random variable X is less than or equal to 4, given that there are 7 trials and the probability of success on each trial is 0.6.

Step 2 ：The binomial distribution is defined as: \[P(X = k) = C(n, k) * p^k * (1-p)^(n-k)\] where: n is the number of trials, p is the probability of success on each trial, k is the number of successes, and C(n, k) is the binomial coefficient, which gives the number of ways to choose k successes out of n trials.

Step 3 ：To find P(X <= 4), we need to sum up the probabilities P(X = 0), P(X = 1), P(X = 2), P(X = 3), and P(X = 4).

Step 4 ：Given that n = 7 and p = 0.6, the calculated probability is approximately 0.5800960000000002.

Step 5 ：Final Answer: The probability that a binomial random variable X is less than or equal to 4, given that there are 7 trials and the probability of success on each trial is 0.6, is approximately \(\boxed{0.5801}\).