# slide4 - Sampling distributions The probability...

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1 Sampling distributions ± The probability distribution of a statistic is called a sampling distribution. ± : the sampling distribution of the mean X n n ... n ... n X ... X X X 2 2 2 2 2 X X n 2 1 σ µ = + + + = = + + + = + + + = 2 The Central Limit Theorem ± When n is sufficiently large (i.e. greater than 15), the sample mean follows approximately a normal distribution: ~, XN n   

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3 Example 1 ± An electronics company manufactures resistors that have a mean resistance of 100 and a standard deviation of 10 . The distribution of resistance is normal. Find the probability that a random sample of n =25 resistors will have an average resistance less than 25 . 4 Example 2 ± Suppose that a random variable X has a continuous uniform distribution Find the distribution of the sample mean of a random sample of size n=40. = otherwise , 0 6 x 4 , 2 / 1 ) x ( f
5 Sampling distribution ± If we have two independent populations with means µ 1 and µ 2 and variance σ 1 2 and σ 2 2 , and if and are the sample means of two independent random samples of sized n 1 and n 2 from these population, then the sampling
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## This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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slide4 - Sampling distributions The probability...

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