Answer:
- A: 88 — 100
- B: 85 — 87
- C: 82 — 84
- D: 80 — 81
- F: 0 — 79
Step-by-step explanation:
You know the relation between X and Z is ...
Z = (X -μ)/σ
Solving for X, we find ...
Zσ +μ = X
You're trying to find the exam scores that correspond to the Z-values you found in question 3.
A = 90th percentile and above = 1.28(8) +78 = 88.24 ≈ 88
B = 80th percentile and above = 0.84(8) +78 = 84.72 ≈ 85
C = 70th percentile and above = 0.52(8) +78 = 82.16 ≈ 82
D = 60th percentile and above = 0.25(8) +78 = 80
So, your blanks are filled like this ...
A: 88 — 100
B: 85 — 87
C: 82 — 84
D: 80 — 81
F: 0 — 79
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Comment on this curve
The setup guarantees that 60% of the class will fail. It is more common to have those below Z = -2 get an F, and those above Z = 2 get an A.
