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≥18), n=20, p=0.9

Answer 1

To find the probability of obtaining 18 or more successes in 20 trials with a probability of success of 0.9, use the binomial probability formula or the binomial cumulative distribution function (CDF).

Step-by-step explanation:

To find the probability P(X≥18) of obtaining 18 or more successes in 20 trials with a probability of success p=0.9, we can use the binomial probability formula or the binomial cumulative distribution function (CDF).

The binomial probability formula is P(X=k) = C(n,k) * p^k * q^(n-k), where C(n,k) is the number of combinations of n trials taken k at a time.

To find P(X≥18), we can find the individual probabilities P(X=18), P(X=19), and P(X=20) and add them together.

Using the binomial probability formula:
P(X=18) = C(20,18) * (0.9)^18 * (0.1)^2 = 20 * 0.9^18 * 0.1^2
P(X=19) = C(20,19) * (0.9)^19 * (0.1)^1 = 20 * 0.9^19 * 0.1^1
P(X=20) = C(20,20) * (0.9)^20 * (0.1)^0 = 0.9^20 * 0.1^0

Then, P(X≥18) = P(X=18) + P(X=19) + P(X=20).