Examine the following probability distribution:

x 5 10 15 20 25 30 35 40 45 50 P(x) 0.01 0.05 0.14 0.20 0.30 0.15 0.05 0.04 0.01 0.05

a. Calculate the expected value and standard deviation for this random variable.

b. Denote the expected value as m. Calculate m - s and m + s.

c. Determine the proportion of the distribution that is contained within the interval m { s.

d. Repeat part c for 112m { 2s and 122m { 3s.