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When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. suppose that a batch of 250 boards has been received and that the condition of any particular board is independent of that of any other board.
a. what is the approximate probability that at least 10% of the boards in the batch are defective?
b. what is the approximate probability that there are exactly 10 defectives in the batch?

Respuesta :

Kalahira
The probability that at least 10% of the boards are defective is: 7.35% The probability of exactly 10 units being defective is: 9.634% With 250 samples the distribution of percent of boards failed can be approximated as a normal distibution. The standard deviation of binomial random variable is sqrt(n*p*(1-p)) where p is the probability of failure. This gives a standard deviation of 3.44601 and 10% deviates from the 5% mean by 1.45 standard deviations. Looking this up on a standard deviation chart shows that 7.35% of 250 unit samples will exceed or meet a 10% failure rate The formula for the probabilty of a certain number of sucesses occuring is (n choose k)*(p^n)*((1-p)^(n-k)) where p is the probability of success n is the number of trials n choose k is the best way i have of writing the binomial coefficient and k is the number of successes the answer is found by letting p=.95 n=250 k=240

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