In preparation for the upcoming school year, a teacher looks at
raw test scores on the statewide standardized test for the students
in his class. Instead of looking at the scores relative to the
norms in the state, the teacher wants to understand the scores
relative to the students who will be in the class. To do so, he
decides to convert the test scores into z-scores relative to the
mean and standard deviation of the students in the class. The mean
test score in his upcoming class is 202, and the standard deviation
is 38.20.
The following are the scores for some (not all) of his students.
Fill in the missing z-scores. Enter z-scores rounded to two decimal
places, and be careful with negative and positive scores.
After that, you'll determine the cutoff scores for z=2.50 and
z=-2.50
Student
Score (X value)
z-score
a
205
0.08
b
199
c
266
1.68
d
222
e
188
-0.37
f
172
g
184
-0.47
h
215
The teacher wants to identify those students who may need an extra
challenge or extra help. As a first cut, he decides to look at
students who have z-scores above z = 2.50 or below z = -2.50.
Identify the test score corresponding to each of the following
z-scores. Round to the nearest whole number.
For z = 2.50, test score = .
For z = -2.50, test score = .