SOLUTION: 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 proba

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Question 1205089: 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≤3)
, n=7
, p=0.6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


given:
P%28X%3C=3%29
n=7
p=0.6

At most 3+successes includes X-values of X=0,1,2,3
To solve this problem, find the sum of the binomial probabilities for each of the values of X, or if there is only one value of X, find the probability of P%28X%29.
In this problem,+P%280%29%2BP%281%29%2BP%282%29%2BP%283%29.

P%280%29=7%21%2F%280%21%287-0%29%21%29%2A0.6%5E0%2A%281-0.6%29%5E%287-0%29=0.0016384
P%281%29=7%21%2F%281%21%287-1%29%21%29%2A0.6%5E1%2A%281-0.6%29%5E%287-1%29=0.0172032
P%282%29=7%21%2F%282%21%287-2%29%21%29%2A0.6%5E2%2A%281-0.6%29%5E%287-2%29=0.0774144
P%283%29=7%21%2F%283%21%287-3%29%21%29%2A0.6%5E3%2A%281-0.6%29%5E%287-3%29=0.193536


answer: P%28X%3C=3%29=0.2898