Answer:
A sample of 139 should be taken.
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 .
That is z with a pvalue of , so Z = 1.96.
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.
Population standard deviation of $3,000.
This means that
How large a sample should be taken if the desired margin of error is $500?
A sample of n is needed.
n is found when M = 500. So
Dividing both sides by 500
Rounding up:
A sample of 139 should be taken.