Question

2. Let's now use Excel to simulate rolling two 6-sided dice and finding the minimum of both dice. • Create a new Excel sheet in your document. Click on cell Al, then click on the function icon f. and select Math&Trig, then select RANDBETWEEN. In the dialog box, enter 1 for bottom and enter 6 for top. • After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner of this first cell, and pull it down the column until 100 cells are highlighted. When you release the mouse button, all 100 random numbers should be present. • Repeat these four steps for the second column, starting in cell BI. • Put the rolled minimum of two dice in the third column: In the first cell of the third column, Type =MIN then highlight the first two cells in the first row, and add ") and click enter. Once you receive the sum of two values in the third cell, drag the lower right corner of this cell, Cl, down to C100. We now have 100 trials of our experiment. • Create a frequency distribution histogram. Copy and paste this histogram in a Word document, and print it out. Make sure to include a title to your histogram. On your print out: (a) make by hand a table of 1-6 on top representing 1 die, and 1-6 down the side rep- resenting the other die. In the table, write the minimum if each row and column number. For example, row 3 and column 4 has a minimum of 3 and row 5 and col- umn 1 has a minimum of 1. Put these numbers in the middle of the table where the row and column meet. This table shows the sample space. (b) Still in your print out, make a chart of each possible minimum, its frequency in your table from (a), and the corresponding probability of such an outcome as a decimal. (c) On your printout of the histogram, draw labeled horizontal lines on each bar repre senting these theoretical probabilities. (d) In your data, for which value of the minimum is the cbserved relative frequency closest to the theoretical probability? Draw an arrow to this value and label as closest on the histogram. (e) Similarly label 'most different for the one that is furthest from the theoretical prob- ability. (f) Write a sentence as to why the observed relative frequencies do not match the theo retical probabilities. (g) Identify the shape of the probability distribution (uniform, bell-curved, right-skewed or left-skewed)

Answer 1

Part 1 - With four steps done

Step 1 - Put the following formula to generate a random number and find the minimum values.

B Min 7 Dice 1 2 = RANDBETWEEN(1,6) 3 = RANDBETWEEN(1,6) 4 = RANDBETWEEN(1,6) 5 = RANDBETWEEN(1,6) 6 = RANDBETWEEN(1,6) = RANDBETWEEN(1,6) 8 = RANDBETWEEN(1,6) 9 = RANDBETWEEN(1,6) 10 = RANDBETWEEN(1,6) 11 = RANDBETWEEN(1,6) 12 = RANDBETWEEN(1,6) 13 = RANDBETWEEN(1,6) 14 = RANDBETWEEN(1,6) 15 = RANDBETWEEN(1,6) 16 = RANDBETWEEN(1,6) 17 = RANDBETWEEN(1,6) 18 = RANDBETWEEN(1,6) 19 = RANDBETWEEN(1,6) 20 = RANDBETWEEN(1,6) 3 6 5 3 1 3 2 1 3 4 5 5 5 3 5 2 2 6 2 Dice 2 = RANDBETWEEN(1,6) 4 = RANDBETWEEN(1,6) 5 = RANDBETWEEN(1,6) 4 = RANDBETWEEN(1,6) 5 = RANDBETWEEN(1,6) 5 = RANDBETWEEN(1,6) 3 = RANDBETWEEN(1,6) 3 = RANDBETWEEN(1,6) 4 = RANDBETWEEN(1,6) 6 = RANDBETWEEN(1,6) 3 = RANDBETWEEN(1,6) 3 = RANDBETWEEN(1,6) 5 = RANDBETWEEN(1,6) 4 = RANDBETWEEN(1,6) 6 = RANDBETWEEN(1,6) 3 = RANDBETWEEN(1,6) 2 = RANDBETWEEN(1,6) 2 = RANDBETWEEN(1,6) 5 = RANDBETWEEN(1,6) 1 =MIN(B2,D2) =MIN(B3,D3) =MIN(B4,D4) =MIN(B5,D5) =MIN(B6,D6) =MIN(B7,07) =MIN(B8,D8) =MIN(B9,D9) =MIN(B10, D10) =MIN(B11,D11) =MIN(B12,012) =MIN(B13,D13) =MIN(B14,D14) =MIN(B15,D15) =MIN(B16,D16) =MIN(B17,D17) =MIN(B18,D18) =MIN(B19,D19) =MIN(B20,D20) 3 24 DAMISTIAN TA DANINCTUAIN1 MAIN441

Step 2 : To create the histogram. Create bins for the dice values.

TJ K Bin

Step 3 : Go to data, click on the data analysis and select histogram.

Help Search Data D raphy Review 21 T Z Sort View Developer 7 Eclear Filter é Reapply Advanced 1 Data Analysis ?, Solver Text to E Outline What-If Forecast Analysis Sheet Columns Sort & Filter Data Tools Forecast Analyze н т т к р м N O P Q Data Analysis X ? | OK OK Cancel Analysis Tools Anova: Two-Factor With Replication Anova: Two-Factor Without Replication Correlation Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram Moving Average Help

Step 4 : Update the values as shown.

G Histogram X ? ок Bin Input C Input Range: $F$2:$F$101 Cancel Bin Range: $J$3:$J$8 | | | بحربي | Labels Help wului $L$3 A B C D E F Dice 1 | Dice 2 Min 5. 3 5 4 3 5 6 6 5 5 5 25 5 4 1 3 5 5 3 3 1 21 31 2 2 3 3 2 5 1 24 1 1 1 3 2 6 3 3 4 4 4 3 33 4 5 3 3 3 3 1 54 55 5 2 5 3 4 4 1 3 4 6 3 6 5 3 3 4 2 2 2 42 26 55 3 2 1 1 3 4 1 1 10 Output options O Output Range: O New Worksheet Ply: O New Workbook 11 12 | NNW wauw w WPN w Wau UNNWW Www WPNWAWU 13 Pareto (sorted histogram) Cumulative Percentage Chart Output 14 15 21

Step 5 : The frequency distribution table will be generated.

L M IN Bin Frequency 1 21 3 4 20 15 More More

Step 6 : Using these result we create the following table and plot the graph. Using insert -> graphs -> bar graph.

0.30 0.25 Interval Frequency Relative Frequency 28 28/100 0.28 21 21/100 0.21 20 20/100 0.20 15 15/100 0.15 14 14/100 0.14 6 2 2/100 0.02 Total 100 1.00 ou AWN 0.20 Probability 0.15 0.10 0.05 0.00 1 2 4 5 6 B Dice value

Done as per instruction in the question

a.

a - Finding the min value when two dice rolled with all possible outcome Dice 1 1 1 6 2 1 3 1 4 1 5 1 1 1 1 2 3 4 1 3 3 2 2 4 3 3 3 3 5 | | 5 5 1 2 4

b.

b Frequency distribution and probability 0.35 0.30 0.25 Interval Frequency Relative Frequency 11 11/36 0.31 9/36 0.25 3 L 7 7/36 0.19 45 5/36 0.14 5 3 3/36 0.08 6 1 1/360.03 Total 36 1.00 Probability 0.10 0.05 0.00 1 2 5 6 3 4 Dice Value

c.

Most Different 0.30 0.28 0.25 Closest Closest Probability 0.15 0.13 0.14 0.10 Closest 0.05 0.02 0.00 Dice value

The blue line represent the theorotical probability.

Accordingly  the closet and the most different is marked