SOLUTION: In a random sample of 5,000 exams, the average score was 500 points with a standard deviation of 90 points. Find the probability that the true mean is between 495 and 500.

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Question 1036404: In a random sample of 5,000 exams, the average score was 500 points with a standard deviation of 90 points.
Find the probability that the true mean is between 495 and 500.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The z-score is = (value-mean)/s/sqrt (n). I'm assuming normality here and don't need a t-test with n=5000.
=(495-500)/90/sqrt(5000)
=-5(sqrt(5000)/90
That is a z between -3.92 and 0 or 49.9955%