8. 8.54 A discrete variable X that can take on integer values from 1 to 10 was sampled 50 times and resulted in the probability estimates shown.

(a) Determine the sample average and standard deviation.

(b) Determine the values 1 and 2 standard deviations from the mean. Of the 50 sample points, how many fall within the two ranges? Xi 1 2 3 6 9 10 P(Xi) 0.2 0.2 0.2 0.1 0.2 0.1