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
PCX > 4), n-8.p -0.7

Answer 1

P(X > 4) = 0.8059

Explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this question, we have that:

`n = 8, p = 0.7`

We want:

`P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)`

In which

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 5) = C_(8,5).(0.7)^(5).(0.3)^(3) = 0.2541`

`P(X = 6) = C_(8,6).(0.7)^(6).(0.3)^(2) = 0.2965`

`P(X = 7) = C_(8,7).(0.7)^(7).(0.3)^(1) = 0.1977`

`P(X = 8) = C_(8,8).(0.7)^(8).(0.3)^(0) = 0.0576`

Then

`P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2541 + 0.2965 + 0.1977 + 0.0576 = 0.8059`

So

P(X > 4) = 0.8059