Assume the random variable X has a binomial distribution wit

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the sample size. Round your answer to 3 decimal places. P(X less than equal to 3)n=6, p= 0.8 PROBABILITY Answer

Solution

P(x = k) = C(n,k) p^k (1? p)^(n? k)

n = 6, p = 0.8
P(x ? 3) = 1 ? P(x > 3)
   = 1 ? P(x = 4) ? P(x = 5) ? P(x = 6)
   = 1 ? C(6,4) (0.8)^4 (0.2)^2 ? C(6,5) (0.8)^5 (0.2)^1 ? C(6,6) (0.8)^6
   = 0.09888