Find the margin of error.
-Thirty randomly selected students took the calculus final. If the sample mean was 78 and the standard deviation was 7.5, construct a 99 percent confidence interval for the mean score of all students.
A) $75.67

Question

Find the margin of error.
-Thirty randomly selected students took the calculus final. If the sample mean was 78 and the standard deviation was 7.5, construct a 99 percent confidence interval for the mean score of all students.
A) $75.67 < \mu < 80.33$
B) $74.63 < \mu < 81.37$
C) $74.23 < \mu < 81.77$
D) $74.24 < \mu < 81.76$

Quizplus · Accepted Answer

The margin of error is calculated using the formula: $ ME = z \times \frac{\sigma}{\sqrt{n}} $. For a 99% confidence interval, the z-score is approximately 2.576. Thus, $ ME = 2.576 \times \frac{7.5}{\sqrt{30}} \approx 3.54 $. The confidence interval is $ 78 \pm 3.54 $, which is $ 74.46 < \mu < 81.54 $. The closest option is C.

Find the Margin of Error 75.67<μ<80.3375.67 < \mu < 80.3375.67<μ<80.33 B) 74.63<μ<81.3774.63 < \mu < 81.3774.63<μ<81.37

Find the Margin of Error $75.67 < \mu < 80.33$ B) $74.63 < \mu < 81.37$