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# Confidence interval using Normal Distribution

Prof. Hardtack gave three exams last semester in a large lecture class. The standard deviation s = 7 was the same on all three exams, and scores were normally distributed. Below are scores for 10 randomly chosen students on each exam. Find the 95 percent confidence interval for the mean score on each exam. Do the confidence intervals overlap? If so, what does this suggest?

Exam 1: 71, 69, 78, 80, 72, 76, 70, 82, 76, 76
Exam 2: 77, 66, 71, 73, 94, 85, 83, 72, 89, 80
Exam 3: 67, 69, 64, 65, 72, 59, 64, 70, 64, 56

#### Solution Preview

Prof. Hardtack gave three exams last semester in a large lecture class. The standard deviation s = 7 was the same on all three exams, and scores were normally distributed. Below are scores for 10 randomly chosen students on each exam. Find the 95 percent confidence interval for the mean score on each exam. Do the confidence intervals overlap? If so, what does this suggest?

Exam 1: 71, 69, 78, 80, 72, 76, 70, 82, 76, 76
Exam 2: 77, 66, 71, 73, 94, 85, 83, 72, 89, 80
Exam 3: 67, 69, 64, 65, 72, 59, 64, 70, 64, 56

Exam 1

71 69 78 80 72 76 70 82 76 76

Total= 750

n= 10

Mean= 75 =750/10

95% Confidence limits

Mean=M = 75

Standard deviation =s= 7

sample size=n= 10

sx=standard ...

#### Solution Summary

95 percent confidence interval for the mean score on 3 exams are calculated. It is also determined whether the confidence intervals overlap.

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