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Answer:
See the explantion below
Step-by-step explanation:
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Assuming the X follows a normal distribution
We know that the margin of error for a confidence interval is given by:
(1)
If we see the formula (1) at the same confidence level, for example 95% and with the same sample size the margin of error just depends of the deviation. If the population deviation for population A is higher than the population deviation for B then A will have more margin of error than B.
On the other case if the deviation for population A is lower than the deviation for population B, then we will have less margin of error for population A than population B.
And the other possible case if both population have the same deviation, then both have equal margin of error.