Question

A company receives 60% of its orders over the Internet. Within a collection of 18 independently placed orders, what is the probability that between eight and ten of the orders are received over the Internet?

Answer 1

To find the probability that between eight and ten of the orders are received over the Internet, use the binomial distribution formula.

Step-by-step explanation:

To find the probability that between eight and ten of the orders are received over the Internet, we need to use the binomial distribution formula. Let's denote the probability of an order being received over the Internet as p = 0.60, the number of trials as n = 18, and the number of orders received over the Internet as X. The probability can be calculated as:

P(8 ≤ X ≤ 10) = P(X = 8) + P(X = 9) + P(X = 10)

Using the binomial distribution formula, where nCx represents the number of combinations of n items taken x at a time, the formula for P(X = x) is:

P(X = x) = nCx * p^x * (1-p)^(n-x)

Substituting the values into the formula and calculating each probability, we get:

P(8 ≤ X ≤ 10) = 18C8 * 0.60^8 * (1-0.60)^(18-8) + 18C9 * 0.60^9 * (1-0.60)^(18-9) + 18C10 * 0.60^10 * (1-0.60)^(18-10)