Question

(Statistics) If variance=16 and n=25 what is the probability that the sample mean takes on a value that is within one unit of the population mean?

Answer 1

If variance is 16, then standard deviation is the square root of it, sigma = 4.

We want the probability that xb (i.e.. the sample mean) is within 1 unit of the population mean, mu.

So we want P( |xb - mu| <= 1 )

Make sense?

Answer 2

do i have to find the z score?

Answer 3

You can do that

P( ( |xb - mu| - 0) / sigma <= 1 ) = P( -1 < =( xb - mu / sigma) <= 1 )

So now, we've normalized and just need the probability that the normal random variate is between -1 and 1 or 2 time the probability that it is between 0 and 1.

Answer 4

I didn't take n into account, we need to use sqrt(var/n) for standard deviation (sigma). So use sigma/sqrt(25) = sigma/5 instead of just sigma.