# If the sample mean is 100, z = 1.85 and sigma_{bar x} = 20, what is the interval estimate for...

## Question:

If the sample mean is {eq}100,\ z = 1.85 {/eq} and {eq}\sigma_{\overline x} = 20 {/eq}, what is the interval estimate for population mean? Also what is the level of confidence?

## Confidence Interval for a Mean:

Confidence interval gives upper and lower bounds true population mean is most likely to be contained plus and minus margin of error from point estimate.

Given that;

{eq}\bar X=100\\z_{crit.}=1.85\\\sigma_{\bar x}=20 {/eq}

Use equation below to find upper and lower limits of the interval:

{eq}\left(\bar X\pm Z_{crit.} \sigma_{\bar x}\right)\\(100\pm 1.85\times 20)\\(100\pm 37)\\(63, 137) {/eq}

The confidence interval is the probability of getting z value between -1.85 and 1.85:

{eq}\begin{align*} P(-1.85\le z\le 1.85)&=P(z<1.85)-P(z<-1.85)\\&=0.9678-0.0322\\&=0.9356 \end{align*} {/eq}

The confidence level is 93.56\%.