SOLUTION: Scores on a standardized exam are known to follow a normal distribution with standard deviation σ = 14. A researcher randomly selects 85 students and computes their average score.

Question 1167442: Scores on a standardized exam are known to follow a normal distribution with standard deviation σ = 14. A researcher randomly selects 85 students and computes their average score. He reports that the mean score is 73.5, with a margin of error of 1.640.
How confident are you that the mean score for all students taking the exam is in the interval (71.86, 75.14)?
Confidence =
%

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The half-interval is 1.64
this equals z*sigma/sqrt(n) or z*14/sqrt(85)
so z=1.64*sqrt(85)/14=1.08 which is at the 86th percentile for z
this would be 28% counting both sides or a CI of 72%.

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