Poisson Distribution
Answer 2

1 - p(0) = (1 - 0.2231) = 0.7769. Barney has better than 3 chances out of 4 of drawing extra KP.

Explanation

Our unit of sampling, our window, is a 75-yard tent. We thus multiply by 75/50 to get the most likely fault rate per tent, which is 1.50. This figure becomes the r in our problem. At that rate, the chance of 0 defects in Barney's tent is found by evaluating the term p(0) = 1.5*0/(0!)(e*1.5). This gives 1/(1)(4.4817) = 0.2231 (see the Table for e*1.5. Or, for that matter, read the final value right off the precalculated Poisson Table). All other outcomes involve at least 1 tent fault, and we may get their joint value by subtracting our p(0) rate from 1 (the total probability). This step yields the answer supplied above, which is 0.7769 = 77.69%, or about 78%. Barney has a better than 75% chance of drawing extra KP.

Comment

That it's not his fault does not matter. Bad luck is also reprehensible.

Statistics is Copyright © 2001- by E Bruce Brooks

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