An institution has 5000 light bulbs put on the morning of everyday. One percent of them go out at the end of the day. Let $X$ denote the number of light bulbs that go out daily. How many light bulbs should be in stock, so that with probability 0.95 all 5000 light bulbs are good at the beginning of everyday ?
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What have you tried? I think the question could be restated as "If you want to make sure that you have a 95% chance of replacing all of the burned out light bulbs on a particular morning, how many light bulbs do you need to have in the stock room?" or "What is the lowest integer $i$ such that $P(X<i)> 0.95$?". – irchans Feb 03 '19 at 01:05
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Yes I tried to approximate the distribution of $X$ to normal distribution, and tried to find $i$ such that $P(X<i)=0.95$ – Pedro Alvarès Feb 03 '19 at 01:12
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That's not a bad approximation. What did you get for the mean and standard deviation of $X$? – irchans Feb 03 '19 at 01:21
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50 for the mean and 49.5 for the variance – Pedro Alvarès Feb 03 '19 at 01:25
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Great. A normally distributed variable will be less than its mean plus 1.64485 standard deviations 95% of the time. Now you just need to compute the mean plus 1.64485 standard deviations. (When I was young, we would look up numbers like 1.64485 in a table. These days I use software.) – irchans Feb 03 '19 at 01:29