Yearly Budget: Bajaj has invested in solar operated lamps. Each lamp has two units: one bulb (to be fixed inside the house) and a solar battery (to be fixed outside). These two units are connected by electrical wire and a switch. Average life of the battery is two years, and that of the bulb is six months. The solar battery, and the bulb can be bought separately (as replacements).

(a) On April 1 (next year) you will fix one such solar operated lamp in your house. Determine the minimum number of lamps you will buy (as replacements) so that you are at least 99% sure of meeting your requirement of lamp in the next financial year.

(b) Suppose on April 1 (next year) 400 households will fix one such solar operated lamp in each household. Determine the minimum number of replacements of bulbs B that will meet total replacements of these 400 households with at least 99% chance during the next financial year.

(c) For these 400 households, it is needed to allocate both bulbs as well as battery sets to meet requirements of replacement during the next financial year. A bulb costs Rupees 500, and a battery costs Rupees 8000. Determine the minimum budget F that will be sufficient for the next financial year with at least 99% chance. (This common budget is for replacements of bulbs, as well as battery sets.)