For your desk lamp, you have an inventory of 25 bulbs

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For your desk lamp, you have an inventory of 25 bulbs. The lifetime of one bulb has an exponential distributionwith mean 1 (in thousands of hours).

(a) What is the exact distribution of the total time you can manage with these 25

bulbs?

(b) Find an approximate probability that you can manage more than 30,000 hours

with these 25 bulbs.