Chapter 12.6, Problem 2CYU

To determine

To Find : The 95% confidence interval of $\overline{x}=72,s=4.6,n=100$ .

Answer to Problem 2CYU

The required confidence interval is $\left(71.0984,72.9016\right)$ .

Explanation of Solution

Given information:

  $\overline{x}=72,s=4.6,n=100$ .

The formula used for 95% confidence interval is,

  $\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}$

The 95% confidence interval for mean is,

  $\begin{array}{l}\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}=72\pm 1.96\cdot \frac{4.6}{\sqrt{100}}\\ \begin{array}{l}=72\pm 0.9016\hfill \\ =\left(71.0984,72.9016\right)\hfill \end{array}\end{array}$

The required confidence interval is $\left(71.0984,72.9016\right)$ .