MAT 144 Top
MAT 144 Topic 5 DQ 1
Technology Assignment 3-1
Complete Technology Assignment 1 in Lesson 3-1 in the textbook. Use the template that is provided in the online resources this lesson. The hint is provided in the video called “Tech Hints QR 3-1.” Fill out the template and upload it ...
Number of sides RollsRolls Outcome
12412 1
84 2
19 3
111 4
512 5
24 6
1210 7
58 8
81 9
118 10
69 11
113 12
Number of Rolls 43Number of Rolls
1000 254000
1010
16
55
75
812
103
83
1211
103
38
114
92
49
1011
121
122
110
109
24
89
1110
112
1012
101
710
410
1012
54Enter the number of sides you want your die to have in cell A2. A number between 2 and 15.The formula in cell B2 randomly generates a number from 1 to the value in cell A2. This simulates rolling a die with the number of sides equal to the value in cell A2. Use the fill-down feature to copy this formula down to give you as many simulated rolls as you want. Think big!
Column D displays the possible outcomes. The "COUNTIF" command in column E counts the number of occurrences of each outcome.
Take these steps:
1. Change the number of sides in A2 to be between 10 and 14, then adjust the number of rows in columns E - J to match.
2. Write a formula to calculate the empirical probabilities in columnS G & I (EP = frequency / # of rolls), using an absolute cell reference to the number of rolls in cell A15 or D15.
3. Write a formula to calculate the theoretical probabilities for each outcome in column J (TP = 1 / # of sides), again using an absolute cell reference to the number of sides in cell A2.
4. Copy the formula in B2 down until you have 1,000 rolls. Note the results in columns F and G.
5. Now, copy the formula in column C2 down until you have 4,000 rolls . Note the results in columns H and I. 6. Compare the empirical probabilities for 1000 rolls iin G against the empirical probabilities for 4000 rolls in column I against the theoretical probabilities in column J. How do the results in column J differ from those in F and H?
Response: Where the theoretical probability is consistent, the numbers vary by a few thousandths in the empirical probability column. They are close to that number, but they never match it completely. This makes sense, because a dice is random, and the theoretical probability suggests that you roll a different number if you roll the dice the number of times equal to the number of sides. (Roll one, you get 1, roll two, you get 2, roll three, a 3, and so on until roll twelve, where you roll a 12).Enter the formula =COUNT(B:B), this will count how many dice rolls you have made. 103
64
108
128
118
910
39
114
1111
68
45
112
103
87
1011
45
32
87
77
1010
119
18
69
103
712
128
34
55
104
38
78
710
412
1110
33
68
38
27
29
28
111
85
43
41
104Column D displays the possible outcomes. The "COUNTIF" command in column E counts the number of occurrences of each outcome.
Take these steps:
1. Change the number of sides in A2 to be between 10 and 14, then adjust the number of rows in columns E - J to match.
2. Write a formula to calculate the empirical probabilities in columnS G & I (EP = frequency / # of rolls), using an absolute cell reference to the number of rolls in cell A15 or D15.
3. Write a formula to calculate the theoretical probabilities for each outcome in column J (TP = 1 / # of sides), again using an absolute cell reference to the number of sides in cell A2.
4. Copy the formula in B2 down until you have 1,000 rolls. Note the results in columns F and G.
5. Now, copy the formula in column C2 down until you have 4,000 rolls . Note the results in columns H and I. 6. Compare the empirical probabilities for 1000 rolls iin G against the empirical probabilities for 4000 rolls in column I against the theoretical probabilities in column J. How do the results in column J differ from those in F and H?
Response: Where the theoretical probability is consistent, the numbers vary by a few thousandths in the empirical probability column. They are close to that number, but they never match it completely. This makes sense, because a dice is random, and the theoretical probability suggests that you roll a different number if you roll the dice the number of times equal to the number of sides. (Roll one, you get 1, roll two, you get 2, roll three, a 3, and so on until roll twelve, where you roll a 12). 114
410
22
78
1112
84
93
105
410
96
16
78
83
43
85
43
105
510
102
1211
13
67
19
109
212
1212
116
72
62
911
47
122
1210
53
32
78
511
710
66
84
91
128
37
91
211 1012
1212
37
74
115
76
16
71
26
66
610
75
115
126
121
38
116
113
71
92
64
510
113
911
64
59
1111
59
118
102
98
73
65
51
65
13
101
412
410
123
212
38
19
38
55
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller KnowledgeBase. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $18.48. You're not tied to anything after your purchase.
