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The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation.  While these are all great books, our only interest for this project is how often each letter is used.  5) a) How many possible ways are there to assign actual letters of the text to the encrypted letters in a message? (Hint: “A” could be assigned to any one of the 26 letters, including itself.  Once “A” has been assigned, “B” can be assigned to any letter except the letter that corresponds to “A”). b) As your answer to part (a) makes clear, there are a super-high number of possible ways all the letters could be assigned.  Knowing something about each letter’s relative frequency dramatically reduces the number of likely combinations.  For example, if there were only 3 possible options for each encrypted letter in the message, then how many possible ways would there be to assign real letters to the letter in the encrypted message?

The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation.  While these are all great books, our only interest for this project is how often each letter is used.  5) a) How many possible ways are there to assign actual letters of the text to the encrypted letters in a message? (Hint: “A” could be assigned to any one of the 26 letters, including itself.  Once “A” has been assigned, “B” can be assigned to any letter except the letter that corresponds to “A”). b) As your answer to part (a) makes clear, there are a super-high number of possible ways all the letters could be assigned.  Knowing something about each letter’s relative frequency dramatically reduces the number of likely combinations.  For example, if there were only 3 possible options for each encrypted letter in the message, then how many possible ways would there be to assign real letters to the letter in the encrypted message?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.4: Two-ways Tables
Problem 12E
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The data file includes the text of three books of the Bible (Joshua, Jonah and Philippians) using the ESV translation.  While these are all great books, our only interest for this project is how often each letter is used. 

5) a) How many possible ways are there to assign actual letters of the text to the encrypted letters in a message? (Hint: “A” could be assigned to any one of the 26 letters, including itself.  Once “A” has been assigned, “B” can be assigned to any letter except the letter that corresponds to “A”).

b) As your answer to part (a) makes clear, there are a super-high number of possible ways all the letters could be assigned.  Knowing something about each letter’s relative frequency dramatically reduces the number of likely combinations.  For example, if there were only 3 possible options for each encrypted letter in the message, then how many possible ways would there be to assign real letters to the letter in the encrypted message?

Letters Frequency Relative Fr Lower Bound Upper Bound Q 5 0.000212 2.63984E-05 0.000398 Z 6 0.000254 5.08478E-05 0.000457 0.000719 0.000377282 0.001061 X 17 J K V B 134 0.005669 0.004711853 0.006626 143 0.00605 0.005061402 0.007039 257 0.010873 0.009550911 0.012195 323 0.013665 0.012184948 0.015145 379 0.016034 0.014432707 0.017635 416 0.0176 0.015923667 0.019276 442 0.018699 0.017127129 0.020271 513 0.021703 0.020041148 0.023365 586 0.024792 0.022809723 0.026774 603 0.025511 0.023500926 0.027521 609 0.025765 0.023745207 0.027785 703 0.029742 0.027576348 0.031908 935 0.039557 0.037072109 0.042042 1097 0.04641 0.043728076 0.049092 1362 0.057622 0.054651246 0.060593 1381 0.058425 0.055434893 0.061415 1407 0.059525 0.05650864 0.062541 1503 0.063587 0.060476159 0.066698 1689 0.071456 0.068172171 0.07474 1810 0.076575 0.073184965 0.079965 2235 0.094555 0.090824791 0.098285 2237 0.09464 0.09090829 0.098372 2845 0.120362 0.11621383 0.12451 23637 Puus C W M Y F U L D R || SZIATO N H E SUM
Transcribed Image Text:Letters Frequency Relative Fr Lower Bound Upper Bound Q 5 0.000212 2.63984E-05 0.000398 Z 6 0.000254 5.08478E-05 0.000457 0.000719 0.000377282 0.001061 X 17 J K V B 134 0.005669 0.004711853 0.006626 143 0.00605 0.005061402 0.007039 257 0.010873 0.009550911 0.012195 323 0.013665 0.012184948 0.015145 379 0.016034 0.014432707 0.017635 416 0.0176 0.015923667 0.019276 442 0.018699 0.017127129 0.020271 513 0.021703 0.020041148 0.023365 586 0.024792 0.022809723 0.026774 603 0.025511 0.023500926 0.027521 609 0.025765 0.023745207 0.027785 703 0.029742 0.027576348 0.031908 935 0.039557 0.037072109 0.042042 1097 0.04641 0.043728076 0.049092 1362 0.057622 0.054651246 0.060593 1381 0.058425 0.055434893 0.061415 1407 0.059525 0.05650864 0.062541 1503 0.063587 0.060476159 0.066698 1689 0.071456 0.068172171 0.07474 1810 0.076575 0.073184965 0.079965 2235 0.094555 0.090824791 0.098285 2237 0.09464 0.09090829 0.098372 2845 0.120362 0.11621383 0.12451 23637 Puus C W M Y F U L D R || SZIATO N H E SUM
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