# Easy Question...need help

#### bootknocker

##### New Member
We need an estimate of the mean acreage of Canadian farms. We plan to measure acreage for a random sample of 100 farms. Results from an earlier study suggest that 200 acres is a reasonable guess for the standard deviation of farm size. Find the probability that the sample mean acreage falls within 10 acres of the population mean acreage.

I am not sure which formula to use for this question. I originally thought that it called for Confidence interval for a mean = ybar +/- z (s/square root of n) But I am not sure. Help ASAP!

#### BioStatMatt

##### TS Contributor
Due to the central limit theorem, we know that a sample mean, ybar, has an approximate normal distribution. In this problem you are given that the variance of this distribution is 200^2. Hence:

(ybar - mu)/200

where mu is the population mean acreage, has an approximate standard normal distribution.

The probability that the sample mean ybar falls within 10 acres of the population mean acreage is:

P(|ybar-mu| < 10) =
P(ybar-mu < 10) - P(ybar-mu < -10) =
P((ybar - mu)/200 < 1/20) - P((ybar - mu)/200 < -1/20) =
P(z < 1/20) - P(z < -1/20)

where z is a standard normal random variable. You can look these last probabilities up in the table in the back of you stat book.

~Matt