Question

in an online store, 8% of the orders are placed by new customers. Let N be the number of orders placed in a day to reach the stores first new customer. Assume each order is customer status is independent. Find the probability that the first new customer place is the fifth order of the day.

Answer 1

The probability that the first new customer places the fifth order of the day is approximately 5.73%, calculated using the geometric distribution formula with a success rate of 8%.

Step-by-step explanation:

The question asks us to find the probability that the first new customer places the fifth order of the day. This scenario follows a geometric distribution model, where the probability that the first success occurs on the k-th trial can be calculated using the formula (1-p)^(k-1) * p, where p is the probability of success on each trial.

In this case, the success is getting an order from a new customer, which happens with a probability of 8% or 0.08. For the first new customer to be the fifth order, we need the first four orders to come from existing customers (failures) and the fifth order to be from a new customer (success).

So the calculation for the probability is as follows:
(1-0.08)^(5-1) * 0.08 = (0.92)^4 * 0.08 = 0.71639296 * 0.08 ≈ 0.0573 or 5.73%.