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Assume a population is normally distributed with a mean of 100 & a standard...

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blendell1 | Student, Undergraduate | eNotes Newbie

Posted January 29, 2012 at 3:11 AM via web

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Assume a population is normally distributed with a mean of 100 & a standard deviation of 15. Would it be unusal for the mean of a sample of 3 to be 115? 

Why or Why Not?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 29, 2012 at 3:43 AM (Answer #1)

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You need to remember the formula of probability in this case of normal distribution such that:P(X>Y)

X denotes the mean of sample of 3

Y= 115

Hence `P(XgtY) = P(Xgt115)`

The mean of sample of 3 needs to be larger than `(X-Y)/sqrt(15^2/3)`

Notice that the standard distribution expresses the square root of variance , hence `P(Xgt=(115-100)/sqrt(15^2/3)) =gt P(Xgt= 2.23) = 0.04`

Hence, since the chances for the mean of a sample of 3 to be 115 are to small, about 4 %, then it would be unusual to happen.

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