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≥10), n=14, p=0.8

Answer #1

Given

n = 14 , p = 0.8

P( X 10) = P( X= 10 ) + P( X=11) + P(X= 12 ) + P( X= 13 ) +P(X= 14)

Using binomial probability

P(X =10) = n!/X!*(n-x)!
*p^{X}*(1-p)^{n-x}

P(X =10) = 14!/10!*4! * (0.8)^{10}*(0.2)^{4} =
0.1720

P(X =11) = 14!/11!*3! *(0.8)^{11}*(0.2)^{3} =
0.2501

P(X = 12) = 14!/12!*2! *(0.8)^{12}*(0.2)^{2} =
0.2501

P( X = 13) = 14!/13!*1! *(0.8)^{13}*(0.2)^{1} =
0.1539

P(X = 14 ) = 14!/14!*0! *(0.8)^{14}*(0.2)^{0} =
0.0440

P( X 10 ) = 0.1729+0.2501+0.2501+0.1539+0.0440

P(X
10) = **0.8702**

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