Students were given an exam with 300 multiple-choice questions. The distribution of the scores was normal and mean was 195 with a standard deviation of 30. You may find it helpful to draw out this distribution before answering the questions below

Question

What were the scores of the students who were within one standard deviation of the mean?

What percent of students did that include?

What was the score of students who scored in the middle of the class? (50% did better, 50% did worse).

If A’s are given to students who score 90% or above, what is the minimum Z-score of someone getting an A?

Let’s say you got 235 on this test. Your colleague is in a different section of this course. Her score was 82 out of 100 on her test. In her section the mean was 72 and the standard deviation was 7. Which one of you did better? (Hint: compare Z-scores.)

Answer 1

Try using the normal distribution tool at
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html

68.27% of the students are within one standard deviation of the mean (165 to 225)

A 90% score would have been 270 correct answers.
Only 0.6% got that score or higher. The Z-score is 2.5 in that case. (2.5 standard deviations above the mean)

Repeat procedure for the second distribution and compare Z-scores

Answer 2

thank you