Question

**How Laude?** Many educational institutions award
three levels of Latin honors often based on GPA. These are
*laude* (with high praise), *magna laude* (with great
praise), and *summa laude* (with highest praise).
Requirements vary from school to school. Suppose the GPAs at State
College are normally distributed with a mean of 2.95 and standard
deviation of 0.49.

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

GPA or higher

Answer #1

(A) given that

mean = 2.95

standard deviation= 0.49

using z percentile table, z score corresponding to top 2% or 98th percentile is 2.054

Required GPA = mean + z*sd

= 2.95 + 2.054*0.49

= 3.96

(B)

given that

mean = 2.95

standard deviation= 0.49

using z percentile table, z score corresponding to top 10% or 90th percentile is 1.282

Required GPA = mean + z*sd

= 2.95 + 1.282*0.49

= 3.58

(C)

given that

mean = 2.95

standard deviation= 0.49

using z percentile table, z score corresponding to top 20% or 80th percentile is 0.842

Required GPA = mean + z*sd

= 2.95 + 0.842*0.49

= 3.36

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