Chapter 8.3, Problem 1.1CYU

To determine

To find: The measurements to have the margin of error of 0.0001.

Answer to Problem 1.1CYU

The measurements are 22.

Explanation of Solution

Given:

Population standard deviation $\left(\sigma \right)=0.0002$

Margin of error ( E ) = 0.0001

Confidence level = 98%

Formula used:

The formula to compute the sample size is:

  $n={\left(\frac{z_{\alpha /2}\times \sigma }{E}\right)}^2$

Calculation:

From the standard normal table, the z-score at 99% confidence level is calculated as:

  $\begin{array}{c}{z}_{\alpha /2}=z_{0.02/2}\\ =2.33\end{array}$

The number of measurements is calculated as:

  $\begin{array}{c}n={\left(\frac{z_{\alpha /2}\times \sigma }{E}\right)}^2\\ ={\left(\frac{2.33\times 0.0002}{0.0001}\right)}^2\\ =21.648\\ \approx 22\end{array}$

Thus, the required number is 22.