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.

good job you smart son of a gun you are smarter that einstein. 7

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right