EXCEL MINITAB TI-84 PLUS TECHNOLOGY Technology 187 Extended solutions are given in the technology manuals that accompany this text. Technical instruction is provided for Minitab, Excel, and the TI-84 Plus. Simulation: Composing Mozart Variations with Dice 1. How many phrases did Mozart write to create the Musical Dice Game minuet? Explain. 2. How many possible variations are there in Mozart’s Musical Dice Game minuet? Explain. 3. Use technology to randomly select a number from 1 to 11. (a) What is the theoretical probability of each number from 1 to 11 occurring? (b) Use this procedure to select 100 integers from 1 to 11. Tally your results and compare them with the probabilities in part (a). 4. What is the probability of randomly selecting option 6, 7, or 8 for the first bar? For all 14 bars? Find each probability using (a) theoretical probability and (b) the results of Exercise 3(b). 5. Use technology to randomly select two numbers from 1 to 6. Find the sum and subtract 1 to obtain a total. (a) What is the theoretical probability of each total from 1 to 11? (b) Use this procedure to select 100 totals from 1 to 11. Tally your results and compare them with the probabilities in part (a). 6. Repeat Exercise 4 using the results of Exercise 5. EXERCISES Wolfgang Mozart (1756–1791) composed a wide variety of musical pieces. In his Musical Dice Game, he wrote a minuet with an almost endless number of variations. Each minuet has 16 bars. In the eighth and sixteenth bars, the player has a choice of two musical phrases. In each of the other 14 bars, the player has a choice of 11 phrases. To create a minuet, Mozart suggested that the player toss 2 six-sided dice 16 times. For the eighth and sixteenth bars, choose Option 1 when the dice total is odd and Option 2 when it is even. For each of the other 14 bars, subtract 1 from the dice total. The minuet shown is the result of the following sequence of numbers. 5 7 1 6 4 10 5 1 6 6 2 4 6 8 8 2 5 9 13 5/11 4/11 6/11 6/11 7/11 10/11 6/11 8/11 1/11 5/11 2/11 8/11 6/11 1/2 4/11 2/2 6 10 14 7 11 15 8 12 16 1 2 3 4
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