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This is the formula for finding the area of a trapezoid
Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.
<h3>What is a z-distribution confidence interval?</h3>The confidence interval is:
In which:
is the sample mean.
- z is the critical value.
- n is the sample size.
is the standard deviation for the population.
The margin of error is given by:
In this problem, we have that the parameters are given as follows:
.
Hence, solving for n, we find the sample size.
Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.
More can be learned about the z-distribution at brainly.com/question/25890103