Scores on an exam were normally distributed. Ten percent of the scores were below 64 and 80% were below 81. Find the mean and standard deviation of the scores.
What will be an ideal response?
A score of 64 is on the 10th percentile, so the z-score of 64 is ?1.28. A score of 81 is on the 80th percentile, so the z-score of 81 is 0.84.
We therefore have the following equations in ? and ?:
Solving for ? and ? yield ?= 74.26, ?= 8.019.
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