A history teacher assigns letter grades on a test according to the following sch

Question

A history teacher assigns letter grades on a test according to the following scheme: Top 10% Scores below the top 10% and above the bottom 60% Scores below the top 40% and above the bottom 20% Scores below the top 80% and above the bottom 10% Bottom 10% Scores on the test are normally distributed with a mean of 69 and a standard deviation of 13.3. Find the numerical limits for each letter grade. A: Above 81: Between 72 and 81 C: Between 58 and 71 D: Between 54 and 57 F: Below 54 A: Above 86 B: Between 72 and 86 C: Between 58 and 71 D: Between 52 and 57 F: Below 52 A. Above 86 B: Between 76 and 86 C: Between 58 and 75 D: Between 52 and 57 F: Below 52 A: Above 81 B: Between 72 and 81 C: Between 58 and 71 D: Between 52 and 57 F: Below 52

Explanation / Answer

mean = 69 and

sd = 13.3

1) A) z of below the top 10% has area under= 0.9 then z=1.28.With all use the formula z=(X-mu)/sigma

1.28=(X-69)/13.3

1.28*13.3=X-69

17.024 =X-69

X=69+17.024 = 86.024 = 86 is A

B) z of above the bottom 60% has area below =0.6 then z=0.25

0.25=(X-69)/13.3

0.25*13.3=X-69

X=3.325 + 69 = =72.325

C) z of below the top 40% has area below 0.6 so z=0.25

So X=72

z of above the bottom 20% has area below = 0.2 so z=-0.84

-0.84=(X-69)/13.3

X=-0.84*13.3+69=57.828 = 58

D)z of below the top 80% has area below 0.2 so z=-0.84

So X=58

z of above the bottom 10% has area below 0.1 so z=-1.28

X = 51.976

F) 52 is F

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.