In one 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 store's first new customer. Assume each order's customer status is independent. Find the probability that the first new customer places the 5th order of the day.
P(N=5)=___

0.0573

Explanation:

Given that:

Percentage of orders placed by new customers = 8%

Proportion of orders placed by new customers, p = 0.08

Using the geometric distribution :

P(n = n) = p * (1 - p)^n-1

Probability that first new customer places the fifth order of the day:

P(n = 5) = 0.08 * (1 - 0.08)^5-1

P(n = 5) = 0.08 * 0.92^4

P(n = 5) = 0.08 * 0.71639296

P(n =5) = 0.0573114368

P(n = 5) = 0.0573