Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
-Thirty randomly selected students took the calculus final. If the sample mean was 75 and the standard deviation was 13.2, construct a 99% confidence interval for the mean score of all students.
A) $68.38

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
-Thirty randomly selected students took the calculus final. If the sample mean was 75 and the standard deviation was 13.2, construct a 99% confidence interval for the mean score of all students. 
A) $68.38 < \mu < 81.62$
B) $70.91 < \mu < 79.09$
C) $68.36 < \mu < 81.64$
D) $69.07 < \mu < 80.93$

Quizplus · Accepted Answer

The 99% confidence interval is calculated using the formula: $ \bar{x} \pm z \times \frac{s}{\sqrt{n}} $. Here, $ \bar{x} = 75 $, $ s = 13.2 $, $ n = 30 $, and the z-value for 99% confidence is approximately 2.576. The interval is $ 75 \pm 2.576 \times \frac{13.2}{\sqrt{30}} $, which results in $ 68.36 < \mu < 81.64 $.

Use the Given Degree of Confidence and Sample Data to Construct