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 5.0 non-work-related e-mails per hour. Assume the arrival of these e-mails is approximated by the Poisson distribution.

What is the probability Linda Lahey, company president, received exactly 4 non-work-related e-mails between 4 P.M. and 5 P.M. yesterday? (Round your probability to 4 decimal places.)

What is the probability she received 6 or more non-work-related e-mails during the same period? (Round your probability to 4 decimal places.)

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

Explanation / Answer

POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.   
x = is the number of independent trials
I.
mean =
= 5
a.
EQUAL
P( X = 4 ) = e ^-5 * 5^4 / 4! = 0.1755
b.
GREATER THAN EQUAL
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-5 * 4 ^ 5 / 5! + e^-5 * 6 ^ 4 / 4! + e^-5 * 4 ^ 3 / 3! + e^-5 * ^ 2 / 2! + e^-5 * ^ 1 / 1! + e^-5 * ^ 0 / 0!
= 0.616,
P( X > = 6 ) = 1 - P (X < 6) = 0.384
c.
LESS THAN EQUAL
P( X < = 4) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-5 * 5 ^ 4 / 4! + e^-5 * 4 ^ 3 / 3! + e^-5 * 4 ^ 2 / 2! + e^-5 * 4 ^ 1 / 1! + e^-5 * ^ 0 / 0!
= 0.4405

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.