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>3), n=4, p=0.8

Please explain how to figure out the P(X>3) thing because that's the part I am struggling really badly on. I have to use excel to calculate my problems. I know it's =BINOM.DIST(?, 4,0.8,TRUE) but the first part of that is stumping me. Can somebody please explain it for me?

For instance, P(X = or > 3) is also confusing on how to choose that answer.

Answer 1

Binom.dist function helps us to calculate the probability value for either X = cases or for X < cases but for X > cases, you need to tweak this formula a little.

Case 1: If in above example, it was x = 3:

Formula: Binom.dist(3, 4, 0.8, False) [Notice the False instead of true, False is used in case if we want the probability only on that specific point and not cumulative probability]

Case - 2: If in the above example, it was x < 3

Formula: Binom.dist(3, 4, 0.8, True)

Case - 3: If in the above example, it was x > 3

Now as per probability rules:

P(X > 3) + P(X < 3) = 1

So,

P(X > 3) = 1 - P(X < 3)

Hence,

Formula for this will be: 1 - Binom.dist(3, 4, 0.8, True)