Question

28 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions.

Use the binomial formula to calculate the probability that exactly five customers make a purchase.

Answer 1

Finall Answer:

The probability that exactly five customers will make a purchase out of six who enter the store can be calculated using the binomial formula.

Step-by-step explanation:

The binomial formula for calculating probabilities in situations with two possible outcomes (success or failure) is
`\(P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^(n - k)\), where \(n\) is the number of trials, \(k\) is the`number of successes
`, \(p\)` is the probability of success on a single trial. In this case,
`\(n = 6\) (number of customers), \(k = 5\)` (number of customers making a purchase), and
`\(p = 0.28\)`(probability of a customer making a purchase). Plugging these values into the formula
`: \(P(X = 5)` =
`\binom{6}{5} \cdot 0.28^5 \cdot (1 - 0.28)^(6 - 5)\).` Calculating this gives the probability that exactly five out of the six customers will make a purchase.