Using four decimal digit accuracy, explain if the respective distribution applie
ID: 3159177 • Letter: U
Question
Using four decimal digit accuracy, explain if the respective distribution applies and, if so determine the probability that at least 5 and at most 7 of 1000 randomly tested micro circuit from a shipment of 25,000 will fall assuming that historically and consistently on average 1 in every 125 tested fails. If it applies, use a Binominal distribution If it applies, use a Poisson distribution If it applies, use a Normal distribution Briefly Explain why statistically the preceding three results differ if they apply and differExplanation / Answer
6.
6.1.
It applies, as the probability of success is constant.
Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)
Here,
x1 = 5
x2 = 7
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 1000
p = the probability of a success = 1/125 = 0.008
Then
P(at most 4 ) = 0.098714991
P(at most 7 ) = 0.452399935
Thus,
P(between x1 and x2) = 0.353684944 [ANSWER]
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6.2
It fails 1 in every 125. So it is a rare event, so we can use a POISSON DISTRIBUTION.
Hence, the mean number of fails every n = 1000 is
u = mean = n p = 1000*(1/125) = 8.
Note that P(between x1 and x2) = P(at most x2) - P(at most x1 - 1)
Here,
x1 = 5
x2 = 7
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 8
Then
P(at most 4 ) = 0.0996324
P(at most 7 ) = 0.452960809
Thus,
P(between x1 and x2) = 0.353328409 [ANSWER]
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6.3.
We cannot use this as n p = 8 < 10. Hence, the sample size is not big enough.
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6.4.
6.1 and 6.2 differ slightly because 6.1 is the exact solution and 6.2 is just an approximation.
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