Suppose you work at a call center that receives customer service calls. On average, your team receives 4 calls per hour. What is the probability of receiving exactly 5 calls during the next hour?

o calculate the probability of receiving exactly 5 calls during the next hour when your team receives an average of 4 calls per hour, you can use the Poisson distribution. The Poisson distribution is often used to model the number of events (in this case, customer service calls) occurring in a fixed interval of time when the events are rare and random. The probability mass function (PMF) of the Poisson distribution is given by: P(X = k) = (e^(-λ) * λ^k) / k! Where: P(X = k) is the probability of receiving k calls. e is the base of the natural logarithm (approximately 2.71828). λ (lambda) is the average rate of events per interval (in this case, 4 calls per hour). k is the number of events you want to calculate the probability for (in this case, 5 calls). Let's calculate it: P(X = 5) = (e^(-4) * 4^5) / 5! P(X = 5) = (2.71828^(-4) * 4^5) / (5 * 4 * 3 * 2 * 1) P(X = 5) ≈ (0.01832 * 1024) / 120 P(X = 5) ≈ 18.73248 / 120 P(X = 5) ≈ 0.1562 So, the probability of receiving exactly 5 calls during the next hour is approximately 0.1562, or about 15.62%.