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Answer:
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{5}{\sqrt{64}} = 1.225[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.225 = 40.775 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.225 = 43.225 minutes
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
The 95% confidence interval for the mean installation time is (40.775, 43.225) and this can be determined by using the formula of margin of error.
Given :
- Standard deviation is 5 minutes.
- Sample size is 64.
- Mean is 42 minutes.
- 95% confidence interval.
The following steps can be used in order to determine the 95% confidence interval for the mean installation time:
Step 1 - The formula of margin of error can be used in order to determine the 95% confidence interval.
[tex]M = z \times \dfrac{\sigma}{\sqrt{n} }[/tex]
where z is the z-score, [tex]\sigma[/tex] is the standard deviation, and the sample size is n.
Step 2 - Now, substitute the values of z, [tex]\sigma[/tex], and n in the above formula.
[tex]M = 1.96 \times \dfrac{5}{\sqrt{64} }[/tex]
[tex]M = 1.225[/tex]
Step 3 - So, the 95% confidence interval is given by (M - [tex]\mu[/tex], M + [tex]\mu[/tex]) that is (40.775, 43.225).
The 95% confidence interval for the mean installation time is (40.775, 43.225).
For more information, refer to the link given below:
https://brainly.com/question/6979326
