Questions: QUESTION 8 - 1 POINT A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x̄=77, with a margin of error of 10. Construct a confidence interval for the mean score (out of 100 points) on the final exam. Provide your answer below:

QUESTION 8 - 1 POINT A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x̄=77, with a margin of error of 10. Construct a confidence interval for the mean score (out of 100 points) on the final exam. Provide your answer below:
Transcript text: QUESTION 8 - 1 POINT A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a $\bar{x}=77$, with a margin of error of 10 . Construct a confidence interval for the mean score (out of 100 points) on the final exam. Provide your answer below: $\square$ $\square$
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Solution

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Solution Steps

Step 1: Given Information

The mean score of the final exam is given as \( \bar{x} = 77 \) and the margin of error is \( E = 10 \).

Step 2: Calculate the Confidence Interval

To construct the confidence interval for the mean score, we use the formula:

\[ \text{Confidence Interval} = \left( \bar{x} - E, \bar{x} + E \right) \]

Substituting the values:

\[ \text{Confidence Interval} = \left( 77 - 10, 77 + 10 \right) = (67, 87) \]

Final Answer

The confidence interval for the mean score on the final exam is \\(\boxed{(67, 87)}\\).

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