Question

The random variable X follows a binomial distribution with n=20 and p=0.6.

a) What is the expected value of X? Your answer should be an integer.

b)

What is the probability X equals 10? Include 4 decimal places in your answer.

c)

What is the probability X is greater than 14? Include 4 decimal places in your answer.

d)

What is the probability that X is no more than 11? Include 4 decimal places in your answer.

e)

What is the probability that X is greater than 8 and less than 13? Include 4 decimal places in your answer.

Answer 1

n = 20, p = 0.6

a)

Expected value, µ = n*p = 20 * 0.6 = 12

b)

Probability of exactly 10, P(X = 10) =

Using excel binomial function:

= BINOM.DIST(10, 20, 0.6, 0)

= 0.1171

c)

Probability of greater than 14, P(X > 14) = 1 - P(X ≤ 14)

Using excel binomial function:

= 1 - BINOM.DIST(14, 20, 0.6, 1)

= 0.1256

d)

Probability of no more than 11, P(X ≤ 11) =

Using excel binomial function:

= BINOM.DIST(11, 20, 0.6, 1)

= 0.4044

e)

Probability between 8 and 13, P(8 < X < 13) = P(X < 13) - P(X ≤ 8) =

= P(X ≤ 12) - P(X ≤ 8)

= BINOM.DIST(12, 20, 0.6, 1) - BINOM.DIST(8, 20, 0.6, 1)

= 0.5276