Steph H.

asked • 02/27/22

A manufacturing machine has a 75% defect rate. If 110 items are chosen at random, answer the following.

A manufacturing machine has a 75% defect rate. If 110 items are chosen at random, answer the following.




d) What is the probability that exactly 79 of them are defective?

  Round final answer to 4 decimal places. 


e) What is the probability that less than 79 of them are defective?

  Round final answer to 4 decimal places. 


f) What is the probability that more than 79 of them are defective?

  Round final answer to 4 decimal places. 


g) What is the probability that exactly 81 of them are defective?

  Round final answer to 4 decimal places. 


h) What is the probability that at least 81 of them are defective?

  Round final answer to 4 decimal places. 


i) What is the probability that at most 81 of them are defective

  Round final answer to 4 decimal places. 


Jon S.

tutor
Have you tried using the formulas for the normal approximation to the binomial distribution?
Report

02/27/22

Stanton D.

My take would immediately be that the probability that this is a realistic question is 0. Yes, you may calculate probabilities here -- but if you have a machine with a 75% failure rate, you take it off-line and repair it.! You *don't* do statistics tests to see if you *might* have some useful product manufactured. There might be some exceptions, if products have inherent variability, and that variability contributes essentially to their value. No examples come to mind to me, however, except possibly induced random mutations on plants. Even in medicine, producing a product that injures some consumers even as it helps others, would be unethical, as we normally calculate these things. There must be a tremendous bias in favor of doing good vs. harm, to justify an intervention. (And scientists and ethicists have a different take on that than do politicians, alas.) 'Nuff said? -- Cheers, --Mr. d.
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02/28/22

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