Suggested languages for you:

Americas

Europe

Q.1.1

Expert-verified
Found in: Page 501

### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

# To assess the accuracy of a laboratory scale, a standard weight known to weigh $10$ grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is $10$ grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about $0.0002$ gram. How many measurements must be averaged to get a margin of error of $0.0001$ with $98%$ confidence? Show your work.

The required number is $22$ .

See the step by step solution

## Step 1: Given information

Given in the question that, To assess the accuracy of a laboratory scale, a standard weight known to weigh $10$ grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is$10$ grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about $0.0002$ gram . We need to find that how many measurements must be averaged to get a margin of error of $0.0001$ with $98%$ confidence.

## Step 2: Explanation

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

Margin of error $\left(E\right)=0.0001$

Confidence level $=98%$

The formula to compute the sample size is:

$n={\left(\frac{{z}_{\alpha /2}×\sigma }{E}\right)}^{2}$

The z-score at $99%$confidence level is calculated from the standard normal table like this,

${z}_{a/2}={z}_{0.02/2}$

$=2.33$

The number of measurements is calculated as:

$n={\left(\frac{{z}_{\alpha /2}×\sigma }{E}\right)}^{2}$

$={\left(\frac{2.33×0.0002}{0.0001}\right)}^{2}$

$=21.648$

$\approx 22$

## Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.