The undergraduate grade point averages (UGPA) of students taking an admissions t

Question

The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure.

55%

5050%

mu equals 3.38=3.38

sigma equals 0.19=0.19

The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure.

(a) What is the minimum UGPA that would still place a student in the top

55%

of UGPAs?(b) Between what two values does the middle

5050%

of the UGPAs lie? 3.3842.76Grade point average

mu equals 3.38=3.38

sigma equals 0.19=0.19

x

Explanation / Answer

Ans:

Given that

mean=3.38

standard deviation=0.19

a)For top 5%

P(Z>z)=0.05

P(Z<=z)=0.95

z=1.645

x=3.38+1.645*0.19

x=3.69

b)middle 50% lie between z=-0.6745 and z=0.6745

lower limit=3.38-0.6745*0.19=3.25

upper limit=3.38+0.6745*0.19=3.51

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