Question

I NEED THIS DONE IN AN EXCEL SPREADSHEET WITH SOLUTIONS

The following probabilities for grades in management science have been determined based on past records:

Grade Probability

A 0.1

B 0.2

C 0.4

D 0.2

F 0.10

The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on.

Determine the expected grade and variance for the course.

Answer 1

Expected Grade=2 i.e., C

Variance=1.2

Explanation:

`Expected\ value=E\left [ x \right ]=\sum _(i=1)^(k) x_(i)p_(i)`

The x values are

A = 4

B = 3

C = 2

D = 1

F = 0

Probability of each of the events

P(4)=0.1

P(3)=0.2

P(2)=0.4

P(1)=0.2

P(0)=0.1

`E\left [ x \right ]=4* 0.1+3* 0.2+2* 0.4+1* 0.2+0* 0.1\\\therefore E\left [ x \right ]=2`

Variance

`Var\left ( x\right)=E\left [ x^2 \right ]-E\left [ x \right ]^2`

`E\left [ x^2 \right ]=4^2 * 0.1+3^2 * 0.2+2^2 * 0.4+1^2 * 0.2+0^2 * 0.1\\\Rightarrow E\left [ x^2 \right ]=5.2\\E\left [ x \right ]^2=2^2=4\\\therefore Var\left ( x\right)=5.2-4=1.2\\`