n establishing warranties on high-definition TV (HDTV) sets, the manufacturer wa
ID: 3204309 • Letter: N
Question
n establishing warranties on high-definition TV (HDTV) sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. However, 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 36.84, with a standard deviation of 3.34 months. Refer to the table in Appendix B.1.
Where should the warranty limits be set so that only 10% of the large-screen TVs need repairs at the manufacturer’s expense? (Round z-score computation to 2 decimal places. Round the final answer to 2 decimal places.)
n establishing warranties on high-definition TV (HDTV) sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. However, 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 36.84, with a standard deviation of 3.34 months. Refer to the table in Appendix B.1.
Explanation / Answer
Since only 10% of the large-screen TVs need repairs at the manufacturer’s expense. We need to find the value at 90% of the curve
hence P(X<x)=0.9
the Z value for the probability of 0.9 can be found from the normal distribution table as 1.28
thus (X-36.84)/3.34=1.28
or X=1.28*3.34+36.84=41.12
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