If a bottling process is working efficiently, the weight of a filled and sealed bottle is...

If a bottling process is working efficiently, the weight of a filled and sealed bottle is normally distributed with a mean of 850 grams and a standard deviation of 3 grams. A bottle is pulled and manually weighed every half hour. The company wants to stop the line if there is strong evidence the machinery is not working right. But, it is costly to stop the line.

a. Based on a sample of only 1 bottle, outside what weight range would you conclude there is a 1% or smaller chance of an observation if the machinery is working correctly?

b. If the machinery is working correctly, and the line operates 14 hours per day, what is the probability of observing 1 or more bottles outside the range you identified in (a) over 5 days of operation?

c. Assuming the company loses lots of money shutting the line down but even more sending out improper product, and based on your work in (a) and (b), suggest a way the company could productively augment their quality control procedure.

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orchestra answered 1 year ago

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