Question

Consider a binomial probability distribution with p= 0.65 and

n=8. Determine the probabilities below.
​a) P(x=2)
​b) P(x<1)
​c) P(x>6)

Answer 1

To determine the probabilities, use the binomial probability formula. a) P(x=2) = 0.296, b) P(x<1) = 0.0024, c) P(x>6) = 0.0139.

Step-by-step explanation:

To determine these probabilities, we can use the binomial probability formula: P(x) = (nCx) * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success on a single trial. Let's calculate the probabilities:

a) P(x=2) = (8C2) * (0.65)^2 * (1-0.65)^(8-2) = 28 * 0.65^2 * 0.35^6 = 0.295928

b) P(x<1) = P(x=0) = (8C0) * (0.65)^0 * (1-0.65)^(8-0) = 1 * 1 * 0.35^8 = 0.00240125

c) P(x>6) = P(x=7) + P(x=8) = (8C7) * (0.65)^7 * (1-0.65)^(8-7) + (8C8) * (0.65)^8 * (1-0.65)^(8-8) = 8 * 0.65^7 * 0.35^1 + 0.65^8 = 0.0139057506