Find the confidence interval specified.
-30 students were randomly selected from a large group of students taking a certain calculus test. The mean score for the students in the sample was 78. Assume that $\sigma = 14.5$. Construct a $99 \%$ confidence interval for the mean score, $\mu$, of all students taking the test.
A)$73.50$ to $82.50$
B) $71.21$ to $84.79$
C) $71.18$ to $84.82$
D) $71.48$ to $84.52$

Question

Find the confidence interval specified.
-30 students were randomly selected from a large group of students taking a certain calculus test. The mean score for the students in the sample was 78. Assume that $\sigma = 14.5$. Construct a $99 \%$ confidence interval for the mean score, $\mu$, of all students taking the test.  
A)$73.50$ to $82.50$
B) $71.21$ to $84.79$
C) $71.18$ to $84.82$
D) $71.48$ to $84.52$

Quizplus · Accepted Answer

The 99% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{\sigma}{\sqrt{n}}$. Here, $\bar{x} = 78$, $\sigma = 14.5$, $n = 30$, and $z$ for 99% confidence is approximately 2.576. The interval is $78 \pm 2.576 \times \frac{14.5}{\sqrt{30}}$, which calculates to approximately $71.18$ to $84.82$.

Find the Confidence Interval Specified σ=14.5\sigma = 14.5σ=14.5 Construct A Interval

Find the Confidence Interval Specified $\sigma = 14.5$ Construct A Interval