Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$. Assume that the population has a normal distribution.
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was $6.6$, construct a $99 \%$ confidence interval for the mean score of all students.
A) $91.68

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$. Assume that the population has a normal distribution.
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was $6.6$, construct a $99 \%$ confidence interval for the mean score of all students.
A) $91.68 < \mu < 98.32$
B) $91.69 < \mu < 98.31$
C) $92.95 < \mu < 97.05$
D) $92.03 < \mu < 97.97$

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as:$95 \pm 2.576 \times \frac{6.6}{\sqrt{30}} = 95 \pm 3.32 = (91.68, 98.32)$

Use the Given Degree of Confidence and Sample Data to Construct