# Thread: Probability of the mean of sample

1. ## Probability of the mean of sample

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?

2. 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?
$\displaystyle |\overline{X} - \mu| > 3$

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

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

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