1. What information does calculating standard deviation provide? How is the z-score related to standard deviation?
2. What values do you need to calculate a z-score?
3. What is the difference between µ and x-?
You are an admissions officer for Harvard Law who has been assigned to evaluate the grade profile for all 22 students admitted to the program. The Law School Admissions Test (LSAT) and Grade Point Average (GPA) Scores for these students are shown below.
|
Student ID
|
LSAT
|
GPA
|
|
1
|
170
|
4.0
|
|
2
|
176
|
3.8
|
|
3
|
172
|
3.78
|
|
4
|
178
|
3.69
|
|
5
|
180
|
3.9
|
|
6
|
168
|
4.0
|
|
7
|
169
|
4.0
|
|
8
|
171
|
3.8
|
|
9
|
174
|
3.74
|
|
10
|
172
|
3.67
|
|
11
|
175
|
3.64
|
|
12
|
169
|
3.92
|
|
13
|
170
|
4.0
|
|
14
|
172
|
3.81
|
|
15
|
173
|
3.74
|
|
16
|
174
|
3.88
|
|
17
|
170
|
4.0
|
|
18
|
172
|
3.8
|
|
19
|
173
|
4.0
|
|
20
|
171
|
3.67
|
|
21
|
180
|
3.67
|
|
22
|
179
|
3.71
|
Using SPSS find µ and σ. Using your findings, calculate the z-scores for the scores below and answer the following questions:
µLSAT:
σLSAT:
µGPA:
σGPA:
4. What is the probability that a student in this class has a GPA below 3.74?
5. What percent of students' GPAs are above 3.90?
6. What percent of students in this class have a GPA between 3.74 and 3.90?
7. What is the probability that a student in this class has an LSAT above 169?
8. What percent of student' LSATs are below 174?
9. What is the probability that a student in this class has an LSAT between 169 and 174?
10. What is the probability that a student in this class has an LSAT between 169 and 172?