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nutcake852 nutcake852
wrote...
Posts: 21
Rep: 1 0
11 years ago
The number of cracks in ceramic tile has a Poisson distribution with a mean of (lambda) = 2.4.

1) What is the probability that a tile has no cracks ?
2) What is the probability that a tile has at least two cracks ?
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wrote...
11 years ago
NOTE: we can use m instead of lambda

Mean = m = 2.4
The general form of Poisson distribution for determining the probability of r successes
P(r) = e^-m * m^r / r!
e^-m = e^-2,4 = e^-2 * e^-0.4
= 0.13534 * o,6703
= 0.0907

1) Probability that a tile has no cracks = P(r=0) = e^-2.4 * 2.4^0 / 0!
  = 0.0907 * 1 / 1
  = 0.0907
2) Probability that a tile has at least two cracks = P(r>1)  OR P(r > or = 2)
= 1 - ( P(r=0) + P(r=1))
P(r=0) = 0.0907
P(r=1) = e^-2.4 * 2.4^1 / 1!
= 0.0907 * 2.4 / 1
= 0.21768
Required probability = 1 - (0.0907 + 0.21768)
= 1 - 30838
= 0.69162
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