A researcher randomly picked 50 students from a small University and found the followings; Average GPA...
A researcher randomly picked 50 students from a small University and found the followings;
Average GPA = 2.8
Variance = 0.04
- Given the information above the researcher calculated that 68% of the 50 students have a GPA between ____________ and ___________.
2. Using the information above, if Lisa has a GPA of 3.5, calculate the Z score for Lisa.
Homework Answers
Solution:
Given, the Normal distribution with,
= 2.8
2
= 0.04
So ,
= 
0.04 =
0.2
1) According to the Empirical rule ,
68% observations lie between
-
and
+
95% observations lie between
- 2
and
+ 2
99.7% observations lie between
- 3
and
+ 3
-
= 2.8 - 0.2 = 2.6
+
= 2.8 + 0.2= 3.0
Answer : 68% of the 50 students have a GPA between 2.6 and 3.0
2)
Lisa has a GPA of 3.5
X = 3.5
Now ,
Z score = (X -
)/
= (3.5 - 2.8)/0.2 = 3.50
z score for Lisa is 3.50
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