Account valuation

A previoius sample had standard deviation $8,200.

How many accounts should be examined to estimate the mean account valuation to within $1,000 with probability 0.95?

The diagram finds the sample size by a trial-and-error method. For any values of n and s, it finds the width of the resulting confidence interval.

Use the bottom slider to set the standard deviation to $8,200. Then drag the sample size slider and verify that n should be 260 or higher to get the '±' value below 1000.

Solving an equation

You could also mention that, provided n is reasonably large (so that the t-value will be approximately 1.96), the equations can be solved to give


A discount brokerage selected a random sample of 36 customer accounts. Their mean total account valuation was $32,000 with standard deviation $8,200.

The resulting 95% CI ($32,000 ± 2,780) was not accurate enough.