The lower and upper limits of the 68.26% confidence interval for the population mean µ, given that n = 64, $$\bar { X }$$ = 110 and $\sigma$= 8, are 109 and 111, respectively.

Question

Quizplus · Accepted Answer

The 68.26% confidence interval for the population mean µ, based on the empirical rule (or one standard deviation from the mean in a normal distribution), can be calculated as $\bar{X} \pm \frac{\sigma}{\sqrt{n}}$. Given $\bar{X} = 110$, $\sigma = 8$, and $n = 64$, the margin of error is $\frac{8}{\sqrt{64}} = 1$. Therefore, the confidence interval is $110 \pm 1$, which is $109$ to $111$, matching the given limits.

The Lower and Upper Limits of the 68 Xˉ\bar { X }Xˉ

The Lower and Upper Limits of the 68 $\bar { X }$