Question 1185618: 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?
Comment on what this probability implies about
whether you think the company is meeting the 3.5 per
sheet defect rate.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! one would expect to see 7 plugs in two sheets.
Poisson parameter 7, see 10 or more
1-poisson cdf (7, 9)=0.1695
rough check is
p(10)=0.7100
p(11)=0.0452
p(12)=0.0263
p(13)=0.0142
p(14)=0.0071
p(15)=0.0033
that sum is 0.1660
If one uses a 5% level, the company is meeting standards.
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