A manufacturing of window frames knows from long experience

A manufacturing of window frames knows from long experience that 1 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment?__________ b. At most one will need adjustment? ________c. More than one will need adjustment? _________ Please again keep three decimals. And keep the \'0\' before the decimal point.

Solution

a)

P(non) = (1-0.01)^20 = 0.817906938 [answer]

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b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.01      
x = the maximum number of successes =    1      
          
Then the cumulative probability is          
          
P(at most   1   ) =    0.983140662 [answer]

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c)

Note that P(more than 1) = 1 - P(at most 1)          
P(at most   1   ) =    0.983140662
          
Thus, the probability of at least   2   successes is  
          
P(more than   1   ) =    0.016859338 [answer]

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