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.

Question

asked Dec 25, 2021 221k views

1 Answer

Henrik Olsson · Answer 1 · 2022-01-01T08:43:59+0000

Answer:

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.