Solve the system of equations.
1 answer:
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We have a piecewise function.
Therefore, to find the function, we must evaluate each domain separately.
We have then:
For
:
The function for this domain is:
For
:
The function for this domain is:
Where,
Substituting:
For
:
The function for this domain is:
Therefore, to find the function, we must evaluate each domain separately.
We have then:
For
The function for this domain is:
For
The function for this domain is:
Where,
Substituting:
For
The function for this domain is:
Answer:
The confidence interval for the mean is given by the following formula:
(1)
And for this case the 95% confidence interval is given by (2.13; 2.37)
We have a point of estimate for the sample mean with this formula:
And for the margin of error we have the following estimation:
Step-by-step explanation:
Previous concepts
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".
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".
represent the sample mean
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
And for this case the 95% confidence interval is given by (2.13; 2.37)
We have a point of estimate for the sample mean with this formula:
And for the margin of error we have the following estimation: