(1 point) Visit the following website: http://www.dicesimulator.com/ and simulate 50 rolls of two dice (or physically roll two dice 50 times) and record your sums in the table below. You may also physically roll two dice 50 times and record your sums.

Roll Sum Roll Sum 1 7 26 7 2 6 27 2 3 4 28 4 4 5 29 1 5 4 30 12 6 3 31 5 7 4 32 11 8 5 33 5 9 7 34 3 10 1 35 7 11 10 36 8 12 9 37 4 13 11 38 6 14 4 39 2 15 7 40 7 16 3 41 8 17 3 42 5 18 5 43 3 19 9 44 5 20 1 45 10 21 12 46 3 22 4 47 2 23 6 48 7 24 2 49 8 25 9 50 4

(1 point) Tally your sums and obtain an empirical probability distribution for the sums when two dice are rolled. Your denominator for the probability portion should be 50 because you performed 50 trials. Sum (x) Frequency of sum: Relative Frequency P(x) Sum (x) Frequency of sum: Relative Frequency P(x) 2 4 0.08 3 6 0.12 4 8 0.16 5 7 0.14 6 3 0.06 7 7 0.14 8 3 0.06 9 3 0.06 10 2 0.04 11 2 0.04 12 2 0.04

(1 points) Use the empirical data to calculate the mean, variance, and standard deviation of this probability distribution. Show all work.

(1 point) Use your results to calculate the empirical probability of rolling a sum less than 3.

(1 point) Use your results to calculate the empirical probability of rolling a sum between (and including) 4 and 7.

(2 points) Compare the results from question 2 to the results from question 7. Do you feel the results are similar? Why or why not? What could be done to make the empirical results even more closely resemble the theoretical?