The following table shows the probability of rolling the numbers 1 through 6 on a fair die.

x 1 2 3 4 5 6
p(x) 1/6 1/6 1/6 1/6 1/6 1/6

what is the standard deviation of the random variable x, "the number that comes up on the die? "

a. 2.917
b. 3.5
c. 1.708
d. 14.028
e. 3.745

First of all find the mean that is:

Mean = (1+2+3+4+5+6)/6 = 3.5

1) Draw a frequency distribution table as shown here below

X                X - Mean      (X-Mean)²

1                1-3.5                 (-2.5)²
2                2-3.5                 (-1.5)²
3                3-3.5                 (-0.5)²
4                4-3.5                 (0.5)²
5                5-3.5                 (1.5)²
6                6-3.5                 (2.5)²
---                           
∑=21         ∑=0                ∑ = 17.5  Note than the number of classes is n= 6

Variance  = σ² = 17.5/6 = 2.917

Standard deviation = √σ²  = √2.917==> σ =1.708 (answer C)