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

To construct a 99% confidence interval for the mean score of all students, we use the formula for the confidence interval: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level, $\sigma$ is the standard deviation, and $n$ is the sample size. For a 99% confidence level, the z-score is approximately 2.576. Plugging in the given values ($\bar{x} = 95$, $\sigma = 6.6$, $n = 30$), we get the interval $95 \pm 2.576\frac{6.6}{\sqrt{30}}$, which calculates to the interval $91.68 < \mu < 98.32$.

Use the Given Degree of Confidence and Sample Data to Construct