How Laude? Many educational institutions award three levels of Latin honors ofte

Question

How Laude? Many educational institutions award three levels of Latin honors often based on GPA. These are cumm laude (with high praise), magna cumm laude (with great praise), and summa cumm laude (with highest praise). Requirements vary from school to school. Suppose the GPAs at State College are normally distributed with a mean of 2.75 and standard deviation of 0.43.

(a) Suppose State College awards the top 2% of students (based on GPA) with the summa cumm laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.

(b) Suppose State College awards the top 10% of students (based on GPA) with the magna cumm laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.

(c) Suppose State College awards the top 20% of students (based on GPA) with the cumm laude honor. What GPA gets you this honor? Round your answer to 2 decimal places.

Explanation / Answer

a) for top 2 percentile ; at 98th percentile critical z =2.0537

therefore corresponding score =mean +z*std deviation =2.75+2.0537*0.43 =3.63

b)for top 10% of students;at 90th percentile critical z =1.2816

therefore corresponding score =mean +z*std deviation =2.75+1.2816*0.43 =3.30

c)

for top 20% of students;at 80th percentile critical z =0.8416

therefore corresponding score =mean +z*std deviation =2.75+0.8416*0.43 =3.11

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