In a previous section of PSY230, the second exam was worth 100 points. The scores from that class were normally
distributed with a mean (μ ) of 75 and a standard deviation (σ) of 5. If the exam scores were converted to a Z distribution, the distribution would form a perfect bell shape. The following questions require locating individual exam scores on the Z distribution and examine the percentage (or proportion) of cases above or below a score.
Hints: It helps to draw a Z distribution (bell curve) and place John's and Tom's Z scores on the distribution for answering the questions. Use the Z table for converting between Z score and area (percentage) of the distribution.
a) Jorge obtained a score of 84. What is Jorge's z score?
b) What is the percentage of the students that scored higher than Jorge?
c) If 60 students were in that class, how many of them scored lower than Jorge's score? (Round your answer to a whole number since we can't have a fraction of a person!)
d) Chris obtained a score of 64. What is Chris's z score?
e) What is the percentage of students that scored between Jorge and Chris?
f) There are 60 students in the class, so how many of them would likely score lower than Chris? (Round your answer to a whole number since we can't have a fraction of a person!)
g) Emma only knows that she scores at 87th percentile on this exam, what is her z score?
h) Based on the result of the previous question, what would be Emma's actual score on the exam?