Question

a cosmetics salesperson, who calls potential customers to sell her products, has determined that 20% of her telephone calls result in a sale. determine the probability distribution for her next three calls. note that the next three calls could result in 0, 1, 2, or 3 sales.

Answer 1

To determine the probability distribution for the salesperson's next three calls, we can use the binomial distribution formula.

Step-by-step explanation:

To determine the probability distribution for the salesperson's next three calls, we can use the binomial distribution formula. The formula is:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

where P(X=k) is the probability of getting k successes (sales) in n trials (calls), p is the probability of success (making a sale), and C(n,k) is the combination or binomial coefficient.

For this problem, we have n = 3 (three calls) and p = 0.20 (probability of making a sale).

1. P(X=0) = C(3,0) * 0.20^0 * (1-0.20)^(3-0) = 0.512
2. P(X=1) = C(3,1) * 0.20^1 * (1-0.20)^(3-1) = 0.480
3. P(X=2) = C(3,2) * 0.20^2 * (1-0.20)^(3-2) = 0.096
4. P(X=3) = C(3,3) * 0.20^3 * (1-0.20)^(3-3) = 0.008