# 05CexS - The Hong Kong University of Science Technology...

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ISMT 111: Business Statistics Solutions for Tutorial Set 5 1. De f ne µ X and σ X be the mean and standard error of the sample mean X respectively. It can shown that µ X = µ and σ X = σ n . (a) µ X = µ =10 and σ X = σ n = 9 25 = 3 5 (b) µ X = µ =4 and σ X = σ n = 4 100 = 1 5 (c) µ X = µ =120 and σ X = σ n = 1 6 = 1 6 =0 . 4082 (d) Ifthesampledpopulationof X in part (a)-(c) are normally distributed, regardless of thesamplesize n , the sampling distribution of X will be exactly normally distributed. If the sampled population are nonnormally distributed: For part (b) as n =100 > 30 , the sampling distribution of X is approximately normally distributed by CLT . For part (a) and (c), as their n< 30 , we could not approximate their sampling distribution of X . 2. µ =50 σ =10 (a) µ X = µ =50 σ X = σ n = 10 100 =1 (b) According to the Central Limit Theorem, as

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05CexS - The Hong Kong University of Science Technology...

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