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. Probability Relative Frequency Histogram Normal Curve P(9.5≤x≤10.5)      P(x≤3)      P(x≥15)      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: Roll Probability 3 1/216 4 3/216 5 5/216 6 10/216 7 15/216 8 21/216 9 25/216 10 27/216 11 27/216 12 25/216 13 21/216 14 15/216 15 10/216 16 5/216 17 3/216 18 1/216   Calculate the theoretical probabilities of the indicated rolls and include them on the table below. Probability Relative Frequency Histogram Normal Curve Theoretical Probability P(9.5≤x≤10.5)        P(x≤3)        P(x≥15)        P(8≤x≤10)

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Chapter1: Combinatorial Analysis
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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.

Probability Relative Frequency Histogram Normal Curve
P(9.5≤x≤10.5)     
P(x≤3)     
P(x≥15)     
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:

Roll Probability
3 1/216
4 3/216
5 5/216
6 10/216
7 15/216
8 21/216
9 25/216
10 27/216
11 27/216
12 25/216
13 21/216
14 15/216
15 10/216
16 5/216
17 3/216
18 1/216

 

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

Probability Relative Frequency Histogram Normal Curve Theoretical Probability
P(9.5≤x≤10.5)       
P(x≤3)       
P(x≥15)       
P(8≤x≤10)       
 
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