Examine the following probability distribution:

a. Calculate the expected value and standard deviation for this random variable.
b. Denote the expected value as μ. Calculate μ – σ and μ + σ.
c. Determine the proportion of the distribution that is contained within the interval μ ± σ.
d. Repeat part c for (1) μ ± 2σ and (2) μ ± 3σ.