Question

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

Answer 1

What do you have to do for part (c)?

Answer 2

Find the standard deviation

Answer 3

Okay, so the std dev is the square root of the variance, or
\[s=\sqrt{s^2}\]
A particularly useful formula for finding the variance is
\[V(X)=E(X^2)-\bigg[E(X)\bigg]^2\]
In other terms,
\[s^2=\sum_{\text{all }x}x^2p(x)-\left(\sum_{\text{all }x}x~p(x)\right)^2\]
Then for the std dev, you would just take the square root.

Answer 4

how did get 8

Answer 5

Given this data, you have
\[s^2=\bigg(4^2\cdot0.20+3^2\cdot0.25+\cdots+0^2\cdot0.15\bigg)-\bigg(2.25\bigg)^2\]

Answer 6

go the same ans but did it different

Answer 7

is that how I get c

Answer 8

Here's what I'm getting:
http://www.wolframalpha.com/input/?i=%28.2*4^2%2B.25*3^2%2B.3*2^2%2B.1*1^2%2B.15*0^2%29-2.25^2

Answer 9

c=1.68 or 1.69