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Q123Section III (Statistics)123 of 190

Group replacement of bulbs: the printed costs make one week optimal

The following failure rates have been observed for certain type of light bulbs:

Week12345Probability of failing by the end of week0.100.250.500.801\begin{array}{l|ccccc} \text{Week} & 1 & 2 & 3 & 4 & 5\\\hline \text{Probability of failing by the end of week} & 0.10 & 0.25 & 0.50 & 0.80 & 1 \end{array}

If the cost of failure replacement is Rs. 20 per bulb and the cost of group replacement is Rs. 500, what is the optimal replacement interval? (Assume that the group has 1000 bulbs.)

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