Probability distribution - histogram, mean, variance & standard deviation

For a probability distribution:

\cdot

mean:\mu = \sum [x \cdot p(x)]

\cdot

variance:\sigma^2 = \sum [(x-\mu)^2 \cdot p(x)]= \sum[x^2 \cdot p(x)] - \mu^2

\cdot

standard\;deviation: \sigma = \sqrt{\sigma^2}= \sqrt{\sum [(x-\mu)^2 \cdot p(x)]} = \sqrt{\sum [(x^2 \cdot p(x)]- \mu^2}

Range Rule of Thumb (Usual VS. Unusual):

\cdot

maximum usual value

= \mu+2\sigma

\cdot

minimum usual value

= \mu-2\sigma

Probability Histogram, Mean, Variance and Standard Deviation
The following table gives the probability distribution of a loaded (weighted) die:

Using calculator commands to find the mean, variance, and standard deviation of the probability distribution.

Based on the "range rule of thumb", determine the outcomes that are considered as "usual" and "unusual".