Probability of the mean of sample

**Yan** · March 8th 2009, 06:33 PM

a random sample of size 100 is taken from a normal population with SD=25. what is the probability that the mean of the sample will differ from the mean of the population by 3 or more either way?

I calculate it as
P(mean of sample - mean >3)=P(Z>3/2.5)

=P(Z>1.2)=0.1151, but the answer is different. can you tell me where did I get wrong?

**mr fantastic** · March 9th 2009, 02:57 AM

Originally Posted by Yan

a random sample of size 100 is taken from a normal population with SD=25. what is the probability that the mean of the sample will differ from the mean of the population by 3 or more either way?

I calculate it as
P(mean of sample - mean >3)=P(Z>3/2.5)

=P(Z>1.2)=0.1151, but the answer is different. can you tell me where did I get wrong?

$|\overline{X} - \mu| > 3$

$\Rightarrow \overline{X} > 3 + \mu$ or $\overline{X} < -3 + \mu$

$\Rightarrow Z > 1.2$ or $Z < -1.2$ .

So the answer will be ${\color{red}2} \Pr(Z > 1.2)$ .

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