The z distribution & stats test scores: Imagine that your lousy statistics profe

Question

The z distribution & stats test scores: Imagine that your lousy statistics professor lost all records of students’ raw scores on the first exam (what a travesty!). However, I did record students’ z scores for the test, as well as the class average of 41 out of 50 points and the standard deviation (SD) of 3 points (treat these as population parameters). Assume your z score is 1.10. SHow your work for each question.

A.What was your percentile score on this exam?

B.Using what you know about z scores and percentiles, how did you do on this exam?

C.What was your original test score?

Explanation / Answer

Answers to the questions with explanation and the formulae is as follows:

The average class score is 41 points

The standard deviation is 3 points

My Z-score is 1.1

A. To know the percentile scores, we need to know where does Z of 1.1 fall. Let check the cumulative area under curve for Z<=1.1

Its coming out to be 86.43% from the Z tables

B. I did fairly well in the exams, better than the median ( 50 percentiles), better than half the class

Also, I did better than 86.43% of people in the scoring

C. Original score was Mean + Z*Standard deviation = 41 + 1.1*3 = 44.3

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