Given the discrete uniform population shown to the right, find the probability that a random sample of size 54, selected with replacement, will yield a sample mean greater than 8.2 but less than 8.9. Assume the means are measured to the nearest tenth.
f(x) = { 1/3, x = 3, 8, 13; 0, elsewhere
The probability is .3068. (Round to four decimal places as needed.)