Sampling

**alrightgeez** · April 22nd 2010, 12:05 PM

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

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 $\sigma$ to make it look like a normal distribution, but I can't see where to go from there.

**CaptainBlack** · April 22nd 2010, 11:28 PM

Originally Posted by alrightgeez

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

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 $\sigma$ to make it look like a normal distribution, but I can't see where to go from there.

You need to use:

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

CB

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