The Weyerhauser Lumber Company headquartered in Tacoma Washi

The Weyerhauser Lumber Company headquartered in Tacoma, Washington, is one of the largest timber and wood product companies in the world. Weyerhauser manufactures plywood at one of its Oregon plants. Plywood contains minor imperfections that can be repaired with small \"plugs.\" One customer will accept plywood with a maximum of 3.5 plugs per sheet on average. Suppose a shipment was sent to this customer and when the customer inspected two sheets at random, 10 plugged defects were counted. What is the probability of observing 10 or more plugged defects if in fact the 3.5 average per sheet is being satisfied? Please show work.

a. .2115

b. .1887

c. .1695

d. .2675

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 maximum of 3.5 plugs per sheet on average.
For 2 sheets it is 3.5*2 = 7

P( X < 10) = P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= e^-7 * 0 ^ 9 / 9! + e^-7 * ^ 8 / 8! + e^-7 * ^ 7 / 7! + e^-7 * ^ 6 / 6! + e^-7 * ^ 5 / 5! + e^-7 * ^ 4 / 4! + e^-7 * ^ 3 / 3! + e^-7 * ^ 2 / 2! + e^-7 * ^ 1 / 1! + e^-7 * ^ 0 / 0!
= 0.8305
P( X > = 10 ) = 1 - P (X < 10) = 0.1695