Answer:
The 90% confidence interval would be given by (57.006;62.994)
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=30 represent the sample size
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 next step would be find the value of ,
,
and
Using the normal standard table, excel or a calculator we see that:
Since we have all the values we can replace:
So on this case the 90% confidence interval would be given by (57.006;62.994)