# Probability Distribution

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:

**RollProbability**31/21643/21655/216610/216715/216821/216925/2161027/2161127/2161225/2161321/2161415/2161510/216165/216173/216181/216

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)