In establishing warranties on HDTV sets, the manufacturer (TopNotch, Inc.) wants
ID: 3130127 • Letter: I
Question
In establishing warranties on HDTV sets, the manufacturer (TopNotch, Inc.) wants to set the limits so that few will need repair at the manufacturer’s expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV, the mean number of months until repairs are needed is 52.58, with a standard deviation of 3.42 months. Where should the warranty limits be set so that only 10 % of the HDTVs need repairs at the manufacturer’s expense? Caroline Hirai is the service manager for TopNotch. Do your calculations in Excel and include a statement to Caroline explaining were the warranty limits should be set and support your answer with statistical evidence.
Show excel steps please
Explanation / Answer
The NORM.INV function will give us the critical value.
=NORM.INV(left tailed area, mean, standard deviation)
Hence, as left tailed area = 0.10, mean = 52.58, standard deviation = 3.42, we type
=NORM.INV(0.10, 52.58, 3.42) [type this on any empty cell]
to get
Critical value = 48.19709365 months [ANSWER]
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We explain to Caroline that the warrantly limit must be set to at most 48.197 months from purchase. This is based on a normal distribution of time before failure of HDTVs with mean of 52.58 moths and standard deviation of 3.42 months.
Only 10% of HDTVs will need repairs before 48.197 months after purchase.