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30. Let L1, …, Ln denote the life-times of n light bulbs. We assume L1, …, Ln to be i.i.d. with mean
u and standard deviation o(Li) = V Var[Lı] = 6 (in months). Use the central limit theorem to
determine approximately the probability that In = 121-1 Li deviates by less than a month from
M, i.e. P[|In – ul < 1], if n = 10.
Hint: You can use freely available calculators for the values of 0(z) (the cumulative distribution
function of N (0,1)) online, see for instance:
https://homepage.divms.uiowa.edu/ mbognar/applets/normal.html
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Tags:
Central Limit Theorem
light bulb
cumulative distribution function
life times
freely available calculators
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