GEOMETRY
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Answer:
The lenght of the interval correspond to:
And since we know the margin of error we can find the limits for the confidence interval:
Step-by-step explanation:
Previous concepts
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".
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
Solution to the problem
Assuming the X follows a normal distribution
The sample mean is distributed on this way:
The confidence interval on this case is given by:
(1)
The margin of error is given by:
The lenght of the interval correspond to:
And since we know the margin of error we can find the limits for the confidence interval: