An internal study by the Technology Services department at Lahey Electronics rev

Question

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of four e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution.

(a) What is the probability Linda Lahey, company president, received exactly one e-mail between 4pm and 5pm yesterday?

(b) What is the probability she did not receive any e-mail during this period?

(c) What is the probability she received ten or more e-mails during the same period?

Explanation / Answer

This problem involves the Poisson distribution, with =4. In the Poisson distribution, the probability of getting exactly x events is:

P[x] = xe-/x!

I plugged this formula into a spreadsheet and calculated from x=0 to x=10.

a. P[1] = 0.0733.

b. P[0] = 0.0183.

c. P[x >= 10] = 1 - P[0] -P[1] - ... - P[9] = 0.0081.

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