Question

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=6, p=0.8

Answer #1

P(X = x) = nCx * p^{x} * (1 - p)^{n-x}

P(X < 4) = 1 - P(X > 4)

= 1 - (P(X = 5) + P(X = 6))

= 1 - (6C5 * 0.8^{5} * 0.2^{1} + 6C6 *
0.8^{6} * 0.2^{0})

= 1 - 0.6554

= 0.3446

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