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 andthe probability of obtaining a success. Round your answer to four decimal places.P(X= 15), n = 18, p = 0.8TablesKeynad



Answer :

Recall that the probability of a binomial distribution is given by

[tex]P(X=x)=^^nC_r\cdot p^x\cdot(1-p)^{n-x}[/tex]

Where n is the number of trials, p is the probability of success, and x is the variable of interest.

nCr is the number of combinations.

For the given case, we have

n = 18

p = 0.8

x = 15

Let us find the probability P(X=15)

[tex]\begin{gathered} P(X=15)=^{18}C_{15}\cdot0.8^{15}\cdot(1-0.8)^{18-15} \\ P(X=15)=816\cdot0.8^{15}\cdot0.2^3 \\ P(X=15)=0.2297 \end{gathered}[/tex]

Therefore, the probability P(X=15) is 0.2297