A machine that makes computer parts has a defect rate of 5%. Assume that each pa

Question

A machine that makes computer parts has a defect rate of 5%. Assume that each part that is made is independent of every other part. Suppose a production run creates 500 computer parts.

a) What are the mean and standard deviation for the number of defective parts created in a single production run?

b) Suppose there were actually 40 parts that were defective in the latest run. Does this lead you to believe that the

c)machine is broken because it is creating too many defective parts? Explain why or why not in terms of the standard deviation.

Explanation / Answer

The Process here can be seen to be following a Binomial distribution with parameteres
n (number of parts in a run) = 500
p (proportion of parts found to be defective) = 0.05

a)
Mean of a binomial distrobution = n*p = 500*0.05 = 25
Variance = n*p*(1-p) = 500*0.05*0.95= 23.75
Standard Deviation = square root (Variance) = 4.8734

b) & c)
Now this can be interpreted as that: you can expect the machine to make almost 25 defective parts per run, and this can have a standard deviation of 4.8734 from the mean, this means that the defective parts should ideally be between 25- 4.87 and 25 + 4.87 ie. between: 20.13 and 29.87; now since the defectiv parts are 40 which is abnormally high in this case, it is possible that the machine is broken and needs replacement!

Thankyou!

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