SOLUTION: Scores on a standardized exam are known to follow a normal distribution with standard deviation = 16. A researcher randomly selects 110 students and computes their average score.

Question 1197916: Scores on a standardized exam are known to follow a normal distribution with standard deviation = 16. A researcher randomly selects 110 students and computes their average score. He reports that the mean score is 74.7, with a margin of error of 1.471.
How confident are you that the mean score for all students taking the exam is in the interval (73.229, 76.171)?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

E = margin of error
E = z*sigma/sqrt(n)
1.471 = z*16/sqrt(110)
1.471 = z*1.525540
z = 1.471/1.525540
z = 0.964249
z = 0.96

Use a calculator like this
https://davidmlane.com/normal.html
to find that P(-0.96 < z < 0.96) = 0.6629 approximately
About 66.29% of the area under the curve is between z = -0.96 and z = 0.96

The confidence level is about 66%

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