The Highway Safety Department wants to study the driving habits of individuals. A sample of 40 cars traveling on a particular stretch of highway revealed an average speed of 69 miles per hour with a standard deviation of 7.8 miles per hour. Round to 4 decimal places.

What sample size is needed to estimate the true average speed to within 2 mph at 99% confidence?

We need a sample size of at least 101

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

What sample size is needed to estimate the true average speed to within 2 mph at 99% confidence?

We need a sample of at least n.

n is found when M = 2. So

Rounding up

We need a sample size of at least 101

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