Question

Let x be a random variable that possesses a binomial distribution with p=0.6 and n=5. Using the

binomial formula or tables, calculate the following probabilities. Also calculate the mean and standard
deviation of the distribution. Round solutions to four decimal places, if necessary.

Answer 1

Let X ~ B(0.6, 5)

Prob of success = 0.6 Prob of failure = 0.4

Amount of samples = 5

P(X
`\geq` 3) = P(3) + P(4) + P(5)

= (5C3 x (0.6)^3 x (0.4)^2) + (5C4 x (0.6)^4 x (0.4)) + (0.6)^5

= 0.6826 (cor to 4 dp)

P(X
`\leq` 4) = P(0) + P(1) + P(2) + P(3) + P(4)

= 1 - P(5)

= 1 - (0.6)^5

= 0.9222 (cor to 4 dp)

P(X = 2) = P(2) = (5C2 x (0.6)^2 x (0.4)^3) = 0.2304

Mean = n x p = 5 x 0.6 = 3

Standard deviation = n x p x ( 1 - p) = 5 x 0.6 x (1 - 0.6) = 5 x 0.6 x 0.4 = 1.2