Question

Records show that the average number of phone calls received per day is 9.2. Find the probability of between 2 and 4 phone calls received (endpoints included) in a given day.

Answer 1

4.76% probability of between 2 and 4 phone calls received (endpoints included) in a given day.

Explanation:

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

`P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)`

In which

x is the number of sucesses

e = 2.71828 is the Euler number

`\mu` is the mean in the given interval.

Records show that the average number of phone calls received per day is 9.2.

This means that
`\mu = 9.2`.

Find the probability of between 2 and 4 phone calls received (endpoints included) in a given day.

`(2 \leq X \leq 4) = P(X = 2) + P(X = 3) + P(X = 4)`

`P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)`

`P(X = 2) = (e^(-9.2)*(9.2)^(2))/((2)!) = 0.0043`

`P(X = 3) = (e^(-9.2)*(9.2)^(3))/((3)!) = 0.0131`

`P(X = 4) = (e^(-9.2)*(9.2)^(4))/((4)!) = 0.0302`

`(2 \leq X \leq 4) = P(X = 2) + P(X = 3) + P(X = 4) = 0.0043 + 0.0131 + 0.0302 = 0.0476`

4.76% probability of between 2 and 4 phone calls received (endpoints included) in a given day.