Question

According to e-mail logs, one employee at a certain company receives an average of 110 emails per week suppose the count of emails received can be adequately modeled as a poisson random variable.

1. What is the probability of this employee receiving exactly 110 emails in a given week?

2. What is the probability of receiving 100 or fewer emails in a given week?

3. What is the probability of receiving more than 125 emails in a given week

4. What is the probability of receiving 125 or more emails in a given week?

5. What is the probability of receiving 200 or fewer emails in a two-week period.

6. What is the probability of receiving 25 or more emails in a word day? Assume the employee works 5 days a week.

Answer 1

Solution;-

Mean = 110

1) The probability of this employee receiving exactly 110 emails in a given week is 0.03801

x = 110

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x = 110) = 0.03801

2) The probability of receiving 100 or fewer emails in a given week is 0.1832.

x = 110

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x < 100) = 0.1832

3) The probability of receiving more than 125 emails in a given week is 0.0721

x = 125

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x > 125) = 0.0721

4) The probability of receiving 125 or more emails in a given week is 0.0855 .

x = 125

By applying poisons distribution:-

P(x; μ) = (e^-μ) (μ^x) / x!

P(x > 125) = 0.0855