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=11), n=18, p=0.8

Answer 1

SOLUTION:

From given data,

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=11), n=18, p=0.8

p=0.8

q = 1-p = 1-0.8 = 0.2

n=18

We know the formula:

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

P(X = 11) = ((18! / 11! (18 - 11)!) * 0.8¹¹ * 0.2^{18 - 11}

P(X = 11) = 31824* 0.8¹¹ * 0.2⁷

P(X = 11) = 31824* 0.085899 * 0.0000128

P(X = 11) = 0.0349

The probability is  0.0349.