A company wants to make up a cheap knock-off of an j-phone. They want the phone

Question

A company wants to make up a cheap knock-off of an j-phone. They want the phone to come with a generous warranty (to lure customers) but not so generous as to cost them a lot of money. They test out 100 prototypes and find they failed, on average, after x = 8000hrs of continuous use. The standard deviation wan sigma = 180hrs.The company wants to be 97.5% confident that the phone won't tail prior to the end of the warranty, i.e. they're willing to pay out on 2.55% of the failures. Note: because of the symmetry of the distribution function, this is like the 95% confidence Interval. How many hours of use should the warranty cover? Calculate your answer and round down to the next even 100.

Explanation / Answer

To have a 95% confidence interval, that means you include everything that is within two standard deviations from the mean. The reason that the problem says to use a 97.5% interval is because by going below the mean, you include everything above the mean, not just two standard deviations from the mean. That extra little bit counts for the extra 2.5%.

To find the waranty limit we take:

x-2=8000hrs-2*180hrs = 7640

Rounding down to the next even hundred would give you 7600 hrs.

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