Question

100 students take a course pass/fail. If they pass they get 4 points towards their GPA, if they fail they get 0. If 90 students pass, what is the mean and standard deviation (to 1 decimal) of the points earned?

Mean: ________a0

Standard Deviation:________ a1

Answer 1

Formulas
Mean = total sum of points / # of data
[Stantard deviation] ^ 2 = {Sum of [every data - mean]^2 } / [number of data - 1]

Procedure:

Mean = total sum of points / # of data

Total sum of points = point of pass + point of fail

points of pass = 90*4 = 360
point of fail = 10*0 = 0
Total sum of points = 360

Number of data = 100

Mean = 360/100 = 3.6

[Stantard deviation] ^ 2 = {Sum of [every data - mean]^2 } / [number of data - 1]

[Sum of every data - mean]^2 = 90*[4 -3.6]^2 + 10* [0 - 3.6]^2 = 14.4 + 129.6 = 144

[Stantard deviation] ^ 2 = [144]/[100-1] =144/99

Standar deviation = √(144/99) = 1.206