Using the z-distribution, a sample size of 180 is needed for the estimate.
<h3>What is a z-distribution confidence interval?</h3>The confidence interval is:
The margin of error is given by:
In which:
is the sample mean.
- z is the critical value.
- n is the sample size.
is the standard deviation for the population.
In this problem, we have a 98% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 2.327.
The population standard deviation is of , and to find the sample size, we have to solve for n when M = 4.
Hence:
n = 179.03.
Rounding up, as a sample size of 179 would result in an error slightly above 4, a sample of 180 is needed.
More can be learned about the z-distribution at brainly.com/question/25890103
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