On average 6 flaws appear in 1000 square yards of fabric man

On average 6 flaws appear in 1000 square yards of fabric manufactured at a textile mill. Find the probability of getting between 35 and 40 flaws in 5000 square yards of fabric produced at the mill On average 6 flaws appear in 1000 square yards of fabric manufactured at a textile mill. Find the probability of getting between 35 and 40 flaws in 5000 square yards of fabric produced at the mill

Solution

A)

Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)          
          
Here,          
          
x1 =    35      
x2 =    40      
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes = 6*(5000/1000) =   30      
          
          
Then          
          
P(at most    34   ) =    0.797308325
P(at most    40   ) =    0.967690426
          
Thus,          
          
P(between x1 and x2) =    0.1703821   [ANSWER]  

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