Question

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

Mean= 3.32

Standard deviation= 0.21

a) What is the minimum UGPA that would still place a student in the top 5% of UGPAs?

b) Between what two values does the middle 50% of the UGPAs lie?

Please explain all answers and thanks in advance!! :)

Answer 1

Mean = = 3.32

Standard deviation = = 0.21

a) We have given P(X > x) = 0.05

z value 0.05 is 1.64

We have to find the value of x

b) We have given the middle 50% of the UGPAs lie.

25% below and 25% above we have to find values.

z value for below 25% is - 0.67

z value for above 25% is 0.67