Answer:
90% confidence interval for the population mean is [tex]149.01,\ 150.99[/tex]
Step-by-step explanation:
Given that, in a random sample of 60 computers, the mean repair cost was $150, with the population standard deviation is $36.
Here,
[tex]n=60,\mu=150,\sigma=36[/tex]
In case of 90% confidence interval, [tex]Z=1.645[/tex]
We know that, the confidence interval will be,
[tex]=\mu\pm Z\dfrac{\sigma}{n}[/tex]
Putting all the values,
[tex]=150\pm 1.645\times \dfrac{36}{60}[/tex]
[tex]=150\pm 0.987[/tex]
[tex]=149.01,\ 150.99[/tex]
The 90% confidence interval for the population mean is (150.98. 149.01).
Confidence Interval In Statistics, a confidence interval is a kind of interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.
In a random sample of 60 computers, the mean repair cost was $150, with the population standard deviation being $36.
The 90% confidence interval for the population mean is given by;
[tex]\rm Confidence \ interval =\mu \pm z\dfrac{\sigma}{n}\\\\Where; \ n = 60 , \ \mu = 150 , \ \sigma = 36\\\\\text{In case of 90 percent confidence interval } Z = 1.6[/tex]
Substitute all the values in the formula;
[tex]\rm Confidence \ interval =\mu \pm z\dfrac{\sigma}{n}\\\\ Confidence \ interval =150 \pm 1.6\dfrac{36}{60}\\\\ Confidence \ interval =150 \pm 0.98\\\\Confidence \ interval = (150 + 0.98, \ 150-0.98)\\\\Confidence \ interval = (150.98, \ 149.01)[/tex]
Hence, the 90% confidence interval for the population mean is (150.98. 149.01).
Learn more about confidence intervals here;
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