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. (with high praise), (with great praise), and (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 highest praise honor.

What GPA gets you this honor? Round your answer to 2 decimal places. GPA or higher

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

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

Explanation / Answer

Ans:

Given that

mean=2.75

standard deviation=0.43

a)P(Z>=z)=0.02

P(Z<=z)=1-0.02=0.98

z=2.054

x=2.75+2.054*0.43=3.63

So,GPA should be 3.63 or higher.

b)P(Z>=z)=0.1

P(Z<=z)=1-0.1=0.9

z=1.282

x=2.75+1.282*0.43=3.30

So,GPA should be 3.30 or higher

c)P(Z>=z)=0.2

P(Z<=z)=1-0.2=0.8

z=0.84

x=2.75+0.84*0.43=3.11

So,GPA should be 3.11 or higher.

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