Standardized Scores (z-scores) WS #2
Name:___________________________
1. Suppose that two graduating seniors, one a marketing major and one an accounting major, are
comparing job offers. The accounting major has an offer for 45,000 per year, and the marketing
student has an offer for 43,000 per year. Summary information about the distribution of offers follows:
Accounting:
mean = 46,000
standard deviation = 1,500
Marketing:
mean = 42,500
standard deviation = 1,000
Relatively speaking which one is the better offer? (find the z-scores of each and explain your reasoning)
2. The average reading speed of students completing a speed-reading course is 450 words per minute
(wpm). If the standard deviation is 70 wpm, find the z score associated with each of the following
reading speeds.
a) 320 wpm
c) 475 wpm
b) 420 wpm
d) 610 wpm
3. Suppose your statistics teacher returned your test results with only a z score written on it. She also
told you that a histogram of the scores was approximately normal, the mean was 81, and the standard
deviation was 5. Use each z score to determine what your actual score was for each of the following:
a) 2.4
d) 0
b) 0.4
e) -2.6
c) 1.8
f) -0.2
4. A student took two national aptitude tests. The national average and standard deviation were 475
and 100, respectively, for the first test and 30 and 8, respectively, for the second test. The student
scored a 625 on the first test and 45 on the second test. Use z scores to determine on which exam the
student performed better relative to the other test takers.
5. A student scores an 85 on a math test with a mean of 75 and a standard deviation of 4. The same
student scores a 90 on a physics test with a mean of 85 and a standard deviation of 3.
a) Sketch a normal curve for each test:
b) Compute the z score for each:
c) On which test do they score better in comparison to the rest of the class? Explain your answer.
6. Ferris has an entrance exam that has a mean of 470 and a standard deviation of 80. Sketch and label
the distribution:
b) Find the z score and percentile for a score of 520
c) Find the z score and percentile for a score of 350
d) If you have a z score of 2.5, what score did you get on the exam?
e) If you have a z score of -0.4, what score did you get on the exam?
f) If you are in the 29th percentile, approximately what score did you get on the exam?