Suppose a representative at car care service center receives a phone call every 4 minutes on average. Find the probability that she receives at least 2 phone calls in 5 minutes (round off to third decimal place).

33.8% probability that she receives at least 2 phone calls in 5 minutes.

Step-by-step explanation:

This question can be solved using the Poisson probability distribution

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Find the probability that she receives at least 2 phone calls in 5 minutes.

Mean of 1 call in 4 minutes.

So what is the mean for 5 minutes?

5/4 = 1.2

We know that in 5 minutes, either she will receive less than two calls, or she will receive at least two calls. The sum of the probabilities of these events is decimal 1. So

We want , which can be represented as:

In which

So

So

33.8% probability that she receives at least 2 phone calls in 5 minutes.

step-by-step explanation: