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 ≤ 3), n = 5, p = 0.2

P(X ≤ 3) = 0.9933.

Step-by-step explanation:

We are given that the random variable X has a binomial distribution with the given probability of obtaining a success

Also, given n = 5, p =0.2.

The above situation can be represented through binomial distribution;

where, n = number of samples (trials) taken = 5

r = number of success = less than equal to 3

p = probability of success which in our question is 0.20.

Let X =  A random variable

So, X ~ Binom(n = 5, p = 0.20)

Now, the probability that X is less than and equal to 3 is given by = P(X ≤ 3)

P(X ≤ 3)  = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

=  

 =    

=  0.9933