590 Too much email According to email logs one employee at y

5.90 Too much email? According to email logs, one employee at your company receives an average of 110 emails per week. Suppose the count of emails received can be adequately modeled as a Poisson random variable.

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

(b) What is the probability of receiving 100 or fewer emails in a given week?

(c) What is the probability of receiving more than 125 emails in a given week?

(d) What is the probability of receiving 125 or more emails in a given week? (Be careful:this is not the same event as in part (c).)

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
company receives an average of 110 emails per week
=110
a)
P( X = 110 ) = e ^-110 * 110^110 / 110! = 0.038

b)
P( X < = 100) = 0.1832
USED AN EXCCEL FORMULA : ROUND(POISSON(100,110,TRUE),4)

c)
USED AN EXCCEL FORMULA : ROUND(POISSON(125,110,TRUE),4)
P( X < = 125) = 0.9279
P( X > 125) = 1 -P ( X <= 125) = 1 - 0.9279 = 0.0721

d)
USED AN EXCCEL FORMULA : ROUND(POISSON(124,110,TRUE),4)

P (X < 125)
P( X > = 125 ) = 1 - P (X < 125) = 0.0855