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.
​(a) What is the minimum UGPA that would still place a student in the top 15​% of​ UGPAs?
​(b) Between what two values does the middle 50​% of the UGPAs​ lie?

mean- 3.28

Standard deviation- 0.17

A normal curve labeled mu = 3.28 and sigma = 0.17 is over a horizontal x-axis labeled Grade point average from 2.56 to 4 in increments of 0.36 and is centered on 3.28.

​(a) The minimum UGPA that would still place a student in the top 15​% of UGPAs is
_______
​(Round to two decimal places as​ needed.)

​(b) The middle 50​% of UGPAs lies between
_____ on the low end and
______ on the high end.
​(Round to two decimal places as​ needed.)

Answer 1

Given

= 3.28

=0.17

Let the minimum UGPA that would still place a student in the top 15​% of UGPAs = x

Now we have

value of Z for top 15% area = 1.0364

a) The minimum UGPA that would still place a student in the top 15​% of UGPAs is 3.46 Answer

For middle 50%

25% left and 25% right from mid

then value of Z are -0.675 and 0.675

also

​(b) The middle 50​% of UGPAs lies between
3.17 on the low end and 3.39 on the high end.