Question

3. Lighthouses are constructed to guide ships travelling in rocky waters and to allow sailing at night. There are many ways to report the size of a lighthouse. However, the height is usually measured from the base of the tower to the top of the ventilator ball. To predict the mean height of all lighthouses in France, we look to randomly select a sample of lighthouses in France. Assume the standard deviation of the size of lighthouses is 8 meters. How large a sample is necessary to ensure that the confidence level is 95% and that the estimated mean height of lighthouses does not differ from the true mean height by more than 1 meter?

Answer 1

n=246 lighthouses

Explanation:

Hello!

You need to calculate the sample size to take to estimate the population mean of french lighthouses height. For this calculation, the information given is the standard deviation (σ=8m), the confidence level 0.95 and a margin of error of 1m.

The formula for the confidence interval is:

x[bar] ±
`Z_(1-\alpha/2)`*(σ/√n)

The margin of error of the interval is:

d=
`Z_(1-\alpha/2)`*(σ/√n)

From this formula you can clear the sample size.

n=(σ * (
`Z_(1-\alpha/2)`/d))²

n=(8 * 1.96)²

1

n =245.86 ≅ 246 lighthouses

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