Question

A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that it mines. Assuming the company reports that the standard deviation of daily output is 200 tons, how many days should it sample so that the margin of error will be 39.2 tons or less?

Answer 1

It should be 100 days sample so that the margin of error will be 39.2 tons or less

Explanation:

We are given that A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that it mines.

`\alpha = 0.05`

To Find two tailed critical value using Z table

`Z_{(\alpha)/(2)}=Z_{(0.05)/(2)}=\pm 1.96`

Margin of error = ME = 39.2

`\sigma = 200`

Formula :
`n = (\frac{Z_{(\alpha)/(2)} * \sigma}{ME})^2`

`n = ((1.96 * 200)/(39.2))^2`

n=100

Hence it should be 100 days sample so that the margin of error will be 39.2 tons or less