Answer:
The confidence interval on this case is given by:
(1)
For this case the confidence interval is given by (62.532, 76.478)[/tex]
And we can calculate the mean with this:
![\bar X = \frac{62.532+76.478}{2}= 69.505](https://tex.z-dn.net/?f=%20%5Cbar%20X%20%3D%20%5Cfrac%7B62.532%2B76.478%7D%7B2%7D%3D%2069.505)
So then the mean for this case is 69.505
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
Assuming the X follows a normal distribution
The confidence interval on this case is given by:
(1)
For this case the confidence interval is given by (62.532, 76.478)[/tex]
And we can calculate the mean with this:
![\bar X = \frac{62.532+76.478}{2}= 69.505](https://tex.z-dn.net/?f=%20%5Cbar%20X%20%3D%20%5Cfrac%7B62.532%2B76.478%7D%7B2%7D%3D%2069.505)
So then the mean for this case is 69.505