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antiseptic1488 [7]
2 years ago
11

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following p

robability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X=14), n=15, p=0.8
Mathematics
1 answer:
ollegr [7]2 years ago
6 0

Use the PMF for the given distribution:

P(X=x) = \begin{cases}\dbinom{15}x 0.8^x (1-0.8)^{15-x} & \text{if } x \in\{0, 1, 2, \ldots, 15\} \\ 0 & \text{otherwise}\end{cases}

Then the probability that X = 14 is

P(X=14) = \dbinom{15}{14} 0.8^{14} 0.2^1 \approx \boxed{0.1319}

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Answer:

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