Grades can be converted into numbers ( as in calculating a gpa where an a=4, b=3,c=2, d=1, and f=0
x grade 4 3 2 1 0
p(x) 0.20 0.25 0.30 0.10 0.15

a. verify that this is a legitimate probability distribution 0.20+0.25+0.30+0.10+0.15=1
b. find the means grade for this class.
4x0.20=0.8
3x0.25=0.75
2x0.30=0.6
1x0.10=0.1
0x0.15=0.0

0.8+0.75+0.6+0.1+0.0=2.25
find the standard deviation
c. 2.25/5=0.45