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)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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