Question

You're a telemarketer selling service contracts for Macy's. You've sold 20 in your last 100 calls (p=.20). If you call 12 people tonight, what's the probability of

A. no sales?

B. Exactly 2 sales?

C. At most 2 sales?

D. At least 2 sales?

please show me how to do it, I have the answers but I don't understand how to get them

Answer 1

a)
Here, n = 12, p = 0.2, (1 - p) = 0.8 and x = 0
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 0)
P(X = 0) = 12C0 * 0.2^0 * 0.8^12
P(X = 0) = 0.0687

b)
We need to calculate P(X = 2)
P(X = 2) = 12C2 * 0.2^2 * 0.8^10
P(X = 2) = 0.2835

c)
P(X <= 2) = (12C0 * 0.2^0 * 0.8^12) + (12C1 * 0.2^1 * 0.8^11) + (12C2 * 0.2^2 * 0.8^10)
P(X <= 2) = 0.0687 + 0.2062 + 0.2835
P(X <= 2) = 0.5584

d)
P(X <= 1) = (12C0 * 0.2^0 * 0.8^12) + (12C1 * 0.2^1 * 0.8^11)
P(X <= 1) = 0.0687 + 0.2062
P(X <= 1) = 0.2749

P(X >=2) = 1 - 0.2749 = 0.7251