# Sampling

• Apr 22nd 2010, 12:05 PM
alrightgeez
Sampling
The mean of a random sample of n observations drawn from an $\displaystyle N(\mu , \sigma^2)$ distribution is denoted by $\displaystyle \bar{x}$. Given that $\displaystyle P(| \bar{x} - \mu | < 0.5\sigma) < 0.05$

Find the smallest value of n.

The only thing I can see to do is divide both sides of the inequality inside the bracket by $\displaystyle \sigma$ to make it look like a normal distribution, but I can't see where to go from there.
• Apr 22nd 2010, 11:28 PM
CaptainBlack
Quote:

Originally Posted by alrightgeez
The mean of a random sample of n observations drawn from an $\displaystyle N(\mu , \sigma^2)$ distribution is denoted by $\displaystyle \bar{x}$. Given that $\displaystyle P(| \bar{x} - \mu | < 0.5\sigma) < 0.05$

Find the smallest value of n.

The only thing I can see to do is divide both sides of the inequality inside the bracket by $\displaystyle \sigma$ to make it look like a normal distribution, but I can't see where to go from there.

You need to use:

$\displaystyle \bar{x} \sim N(\mu,\sigma^2/n)$

CB