A population has a mean of 50 and a standard deviation of 16. If a random sample of 49 is taken, what is the probability that the sample mean is each of the following?
a. Greater than 57

Question

anonymous · Answer

Impossible to answer without information about the distribution.

zarkon · Answer

I'm sure they are supposed to use the central limit theorem here.

anonymous · Answer

^what he said

zarkon · Answer

$$P(\overline{x}>57)=P\left(\frac{\overline{x}-50}{16/\sqrt{49}}>\frac{57-50}{16/\sqrt{49}}\right)$$

then by clt

$$=P\left(Z>3.0625\right)=1-P(Z\le3.0625)=\cdots$$