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Unformatted text preview: . 5 z Z P 0.25 [0.501,0.545] 0.3 [0.728,0.766] 0.35 [0.854,0.883] 0.4 [0.952,0.969] d) We have z P{N<z} 0.25 0.5 0.3 0.725747 0.35 0.88493 0.4 0.96407 See the accompanying spreadsheet for the calculations. These probabilities are close to the probabilities estimated in Part c. n Z is the average of n i.i.d. random variables. Therefore, by the central limit theorem, the distribution of n Z converges to the normal distribution as n approaches infinity. For a finite and large n , the distribution of n Z is approximately normal. Interestingly, for the central limit theorem to take effect, n =5 is large enough....
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 '08
 TOPALOGLU

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