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Hi,

I'm working on the following problem:

"Home tub and shower stalls are made of composite materials in a production process that involves laying up fibres, spraying resin, and moulding. Defects such as micro cracks (in spider web patterns) often appear in the final products. Although these defects do not affect the performance of the product, they are unappealing to customers. The number of defects per unit, Y, is a random variable that follows the Poisson distribution with mean lambda =0.9

(a) Find the probability that a tub and shower unit will have between one and four (inclusive) defects.

(b) Find the probability that a production run of 100 units will have at least 40 defect free units."

For a) I looked up the P(x < 1) and P(x < or =  4) in the stats table for lambda 0.9 and got 0.4066 and 0.9977 respectively so by my calculations the probability of having between 1 and 4 inclusively defects is 0.591.

I cannot however figure out how to get the answer for b)using the statistics table as x only goes up for 8 for lambda 0.9. I would really appreciate some help with this.

Thanks in advance.

Answer
The second part of the problem uses a binomial distribution. You can figure out the probability that a single tub has no defects from your table, I don't see why you need to "go past 8" on your table, you are interested in the probability that the number of defects is <1. A similar problem is solved here:

http://mathhelpforum.com/statistics/173710-poisson-binomial-distribution-clarifi

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