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

Answer 1

Recall that the probability of a binomial distribution is given by

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)

`\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}`

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