Question

the number of people calling the call centre in any one hour period follows a p(10) distribution. what is the probability that among the customers calling in the next hour, none of them has to wait more than hour to be connected with a person?

Answer 1

To find the probability that none of the customers have to wait more than an hour to be connected with a person, we can use the probability mass function (pmf) of the Poisson distribution. By calculating the sum of the individual probabilities, we can determine the overall probability.

Step-by-step explanation:

To solve this problem, we need to use the probability mass function (pmf) of the Poisson distribution.

The probability mass function of a Poisson distribution with mean lambda is given by P(X = k) = (e^(-lambda) * lambda^k) / k!, where X denotes the random variable representing the number of customers calling the call centre in the next hour, and k represents the number of customers.

In this case, we want to find the probability that none of the customers have to wait more than an hour to be connected with a person. This means we need to find the probability that the number of customers, X, is less than or equal to 60.

P(X ≤ 60) = P(X = 0) + P(X = 1) + ... + P(X = 60)

To calculate each individual probability, we can use the formula mentioned above and substitute the value of lambda, which is 10 in this case. We can then calculate the sum using a calculator or software.

The final result will give us the probability that none of the customers have to wait more than an hour to be connected with a person.