Construct an experimental, discrete probability table by rolling three six-sided dice and calculating the total. Perform 200 trials and record the results. The rolling of three six-sided dice can be simulated using a graphing calculator by “rolling” each of the dice in a separate list using:

                        Math –> Prob –> randInt(1, 6, 200)

Once all three lists are generated, add them to create the totals of the 200 trials.

• Create a discrete random variable relative frequency histogram for this data. Clearly label the axes and scale.
• Calculate the mean and standard deviation for the roll totals:

????=μ=   ????=σ= 

      Use these to define a normal probability distribution for the total on the roll of 3 dice.

• Compare the probabilities of the experimental discrete probability distribution and the normal curve distribution for several cases listed on the table. Complete the table.

ProbabilityRelative Frequency HistogramNormal Curve????(9.5≤????≤10.5)P(9.5≤x≤10.5) ????(????≤3)P(x≤3) ????(????≥15)P(x≥15) ????(8≤????≤10)P(8≤x≤10) 

• Write a brief paragraph comparing the results of the table above. Discuss any similarities or differences in these results.
• There are 216 possible outcomes for the roll of three dice. The theoretical probabilities for the outcomes of the roll of three six-sided dice are:

RollProbability31/21643/21655/216610/216715/216821/216925/2161027/2161127/2161225/2161321/2161415/2161510/216165/216173/216181/216

Calculate the theoretical probabilities of the indicated rolls and include them on the table below.

ProbabilityRelative Frequency HistogramNormal CurveTheoretical Probability????(9.5≤????≤10.5)P(9.5≤x≤10.5) ????(????≤3)P(x≤3) ????(????≥15)P(x≥15) ????(8≤????≤10)P(8≤x≤10)