Roll a ten sided die

Part A:

Theoretically, if you roll a 10 sided die and variable x is the outcomes, the possible values that x can take are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

1. Write the probability distribution of x. These probabilities are the Classical (or the Theoretical) probabilities( Chapter 5)
2. Calculate mean, variance and standard deviation of x(using the probability distribution). ( Chapter 5)

Part B – Using Excel:      

Let us assume you are rolling a 10 sided die25 times, 200 times and 1000 times. So you will have three data sets. To get the data you do not have to roll a die, use EXCEL with the command =RANDBETWEEN(1,10). Which will give you a random number between 1 and 10. Copy this 25, 200 and 1000 times to get the three data sets.

1. Prepare a frequency distribution table, using x as the outcomes 1, 2, 3, 4, 5,6, 7, 8, 9,& 10.  (Chapter 2)
2. Calculate relative frequencies. ( Chapter 2)
3. Calculate the percentages. (Chapter 2)
4. Draw a bar graph for the frequency distribution. (Chapter 2)
5. Draw a dot plot for the frequency distribution. (Chapter 2)
6. Draw a pie chart. (Chapter 2)
7. Calculate sample mean, mode, variance and standard deviation for each data set. (Chapter 3)
8. Calculate the three Quartiles, the IQR and Prepare a Box-and-Whisker plot. (Chapter 3)
9. Find the Probability for each x ( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) using relative frequency.

(Relative frequencies will give P(1), P(2), ……P(10).  Where P(2) is the probability that the outcome is 2 These values are the Empirical (or the Experimental) Probabilities.)     (Chapter 4)

Part C : 

Lets compare Part A values with results you got for Part B ( for each of the data set)

1. Compares the Probabilities. (Part A-1 and Part B -9 )
2. Compare the Mean, Variance and the standard deviation. (Part A-2 and Part B-7)

Part D :

For all the three data sets find the 95% confidence interval for µ using. (Chapter 8)

1. The population standard deviation found in Part A – 2 and the Z-distribution.
2. The Sample standard deviation found in Part B-7 and the t-distribution

Part E:

Conclusion

Write about your findings, mainly discuss how the shapes of the graph and the sample statistics change as the sample size increase? (You can write the conclusion at the end of the project or at the end of each graph or findings.)

• I will show you step by step how to do the project during the class.
• The final report should be a word document, template of which I have attached on blackboard. You need to copy all the graphs and tables from your  EXCEL file to the word document.
• You need to submit both the Excel file ( 50 points) and the report ( 50 points)
• You can start from Part B as it’s from Chapter 2.
• Important – When you get the data sets in Part B using the function RANDBEWTEEN, make sure that you copy these values (Values only) , before you do the calculations, otherwise every time you press enter the values will change as it will generate a new set of random numbers.