The number of flows in bolts of cloth in textile manufacturi

The number of flows in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean of 0.1 flow for square meter. What is the probability that three flaws in one square meter of cloth? What is the probability that there is one flow in 10 square meters of cloth? What is the probability that there is no flaws in 15 square meters of cloth? What is the probability that there are at least flaws in 10 square meters of cloth?

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    0.1      
          
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.000150806 [ANSWER]

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b)

In 10 square meters, there are 0.1*10 = 1 flaw on the average.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    1      
          
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.367879441 [ANSWER]

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c)

In 15 sq. m., there are 0.1*15 = 1.5 flaws on the average.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    1.5      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.22313016 [ANSWER]

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d)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    1      
          
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.735758882
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.264241118 [ANSWER]