An internal study by the Technology Services department at L

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 3.8 non-work-related e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution.

c. What is the probability she received two or less non-work-related e-mails during the period? (Round your answer to 4 decimal places.)

b. What is the probability she received 6 or more non-work-related e-mails during the same period?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)
= e^-3.8 * 3.8 ^ 2 / 2! + e^-3.8 * 3 ^ 1 / 1! + e^-3.8 * ^ 0 / 0!
= 0.2689

b)

P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-3.8 * 3 ^ 5 / 5! + e^-3.8 * ^ 4 / 4! + e^-3.8 * ^ 3 / 3! + e^-3.8 * ^ 2 / 2! + e^-3.8 * ^ 1 / 1! + e^-3.8 * ^ 0 / 0!
= 0.8156
P( X > = 6 ) = 1 - P (X < 6) = 0.1844