The qualitycontrol inspector of a production plant will reje

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of nine syringes taken from the batch. Suppose the batch contains 5% defective syringes.

What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.)

(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)


(d) Find . (Round your answer to three decimal places.)

Solution

a)

What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.)

E(x) = n p = 9*0.05 = 0.45 [answer]

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c)

(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)

For a batch to be accepted, less than 2 syringed must be defective.

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    9      
p = the probability of a success =    0.05      
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   ) =    0.928788604
          
Which is also          
          
P(fewer than   2   ) =    0.928788604 = 0.929 [answer]

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d)

As

sigma = sqrt[n p (1 - p)].

sigma = sqrt(9*0.05*(1-0.05)) = 0.653834842 = 0.654 [answer]