I'm having a difficult time figuring this out... confused on how to go about solving, & which formula/steps to use....


A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is?

Hi ecohelp,

First you want to find se_Xbar, the standard error of sample mean.

se_Xbar
=sd/sqrt(n)
=24/sqrt(64)
=3

Then you can standardize the sample mean and find the probability.

P(183 < Xbar < 186)
=P[(183-mu)/se_Xbar < (Xbar-mu)/se_Xbar < (186-mu)/se_Xbar]
=P[(183-180)/3 < Z < (186-180)/3]
=...

Let me know if you have further questions.