While these are all great books, our only interest for this project is how often each letter is used.

1) In the Word file containing the Biblical text, use the "Find" feature to identify how many times each letter occurs (i.e. the letter's frequency).Make an Excel spreadsheet to display the number of occurrences of each letter in the English alphabet.(10 points)

2) In the Excel spreadsheet, sum your frequencies to compute the total number of letters in the 3 books (this is n).

a) In your spreadsheet, use the formula p =X/nto compute the sample proportion of each letter's appearances relative to total number of letters (i.e. find the relative frequency of each letter).Use the Excel sorting function to sort the letters in order of their frequencies.(6 points)

b) The simple Confidence Interval (CI) formula(p -1.96((p q )/n),p +1.96((p q )/n) to find a 95% CI on the proportion of how often each letter is used in English text in general.Enter the lower bound in the first Excel column (using p -1.96((p q )/n)) and the upper bound in the next column (usingp +1.96((p q )/n) ).(8 points)

3)Identify those letters where Cls do not overlap with any the CIs of any of the other letters.(For example the CI [0.042, 0.052] overlaps with [0.050, 0.060] because the upper bound of the first CI is greater than the lower bound of the second CI.)List the letters with the non-overlapping Cis and specify how many such letters there are.(6 points)

4) The previous analysis could be useful if our goal was to decipher an encrypted message, where each letter is scrambled (for example, each "a" might become a "g", while each "b" might become an "o" and so forth).

a) Assume that the letter "z" in encrypted message has a relative frequency of 0.09 (it accounts for 9% of the total number of letters).Which letter's Confidence Intervals from question 2 include 0.09 and thus are the most likely candidates to be the letter which was encrypted as "z"? (4 points)

b) Further assume that "y" in the encrypted message has a relative frequency of 0.055 (5.5%).Which letter's question 2 CIs include 0.055? (4 points)

c) If "x" in the encrypted message has a relative frequency of 0.025 (2.5%), which letter's question 2 CIs include 0.025? (4 points)

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").(4 points)

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?(4 points)

------------------------------------------------------- 1After the death of Moses theservant of theLord, theLordsaid to Joshua the son of Nun, Moses'assistant,²"Moses my servant is dead. Now therefore arise, go over this Jordan, you and all this people, into the land that I am giving to them, to the people of Israel.³Every place that the sole of your foot will tread upon I have given to you, just as I promised to Moses.⁴From the wilderness and this Lebanon as far as the great river, the river Euphrates, all the land of the Hittites to the Great Sea toward the going down of the sun shall be your territory.⁵No man shall be able to stand before you all the days of your life. Justas I was with Moses, soI will be with you.I will not leave you or forsake you.⁶Be strong and courageous, for you shall cause this people to inherit the land that I swore to their fathers to give them.⁷Only be strong andvery courageous, being careful to do according to all the lawthat Moses my servant commanded you.Do not turn from it to the right hand or to the left, that you may have good success wherever you go.⁸This Book of the Law shall not depart from your mouth, butyou shall meditate on it day and night, so that you may be careful to do according to all that is written in it. For then you will make your way prosperous, and then you will have good success.⁹Have I not commanded you?Be strong and courageous.Do not be frightened, and do not be dismayed, for theLord your God is with you wherever you go."

¹⁰And Joshua commanded theofficers of the people,¹¹"Pass through the midst of the camp and command the people, 'Prepare your provisions, forwithin three daysyou are to pass over this Jordan to go in to take possession of the land that theLordyour God is giving you to possess.'"

¹²And to the Reubenites, the Gadites, and the half-tribe of Manasseh Joshua said,¹³"Remember the word thatMoses the servant of theLord commanded you, saying, 'TheLordyour God is providing you a place of rest and will give you this land.'¹⁴Your wives, your little ones, and your livestock shall remain in the land that Moses gave you beyond the Jordan, but all the men of valor among you shall pass over armed before your brothers and shall help them,¹⁵until theLordgives rest to your brothers as he has to you, and they also take possession of the land that theLordyour God is giving them.Then you shall return to the land of your possession and shall possess it, the land that Moses the servant of theLordgave you beyond the Jordan toward the sunrise."

¹⁶And they answered Joshua, "All that you have commanded us we will do, and wherever you send us we will go.¹⁷Just as we obeyed Moses in all things, so we will obey you. Only may theLordyour Godbe with you, as he was with Moses!¹⁸Whoever rebels against your commandment and disobeys your words, whatever you command him, shall be put to death.Only be strong and courageous."

2And Joshua the son of Nunsenttwo men secretly from Shittim as spies, saying, "Go, view the land, especially Jericho." And they went and came into the house ofa prostitute whose name wasRahab and lodged there.²And it was told to the king of Jericho, "Behold, men of Israel have come here tonight to search out the land."³Then the king of Jericho sent to Rahab, saying, "Bring out the men who have come to you, who entered your house, for they have come to search out all the land."⁴But the woman had taken the two men and hidden them. And she said, "True, the men came to me, but I did not know where they were from.⁵And when the gate was about to be closed at dark, the men went out. I do not know where the men went. Pursue them quickly, for you will overtake them."⁶But she had brought them up to the roof and hid them with the stalks of flax that she had laid in order on the roof.⁷So the men pursued after them on the way to the Jordanas far as the fords. And the gate was shut as soon as the pursuers had gone out.

⁸Before the menlay down, she came up to them on the roof⁹and said to the men, "I know that theLordhas given you the land,and that the fear of you has fallen upon us, and that all the inhabitants of the landmelt away before you.¹⁰For we have heard how theLorddried up the water of the Red Sea before you when you came out of Egypt, andwhat you did to the two kings of the Amorites who were beyond the Jordan, toSihon and Og, whom you devoted to destruction.¹¹Andas soon as we heard it,our hearts melted, and there was no spirit left in any man because of you, fortheLordyour God, he is God in the heavens above and on the earth beneath.¹²Now then, please swear to me by theLordthat, as I have dealt kindly with you, you also will deal kindly with my father's house, andgive me a sure sign¹³that you will save alive my father and mother, my brothers and sisters, and all who belong to them, and deliver our lives from death."¹⁴And the men said to her, "Our life for yours even to death! If you do not tell this business of ours, then when theLordgives us the landwe will deal kindly and faithfully with you."

¹⁵Then shelet them down by a rope through the window, for her house was built into the city wall, so that she lived in the wall.¹⁶And she saidto them, "Go into the hills, or the pursuers will encounter you, and hide there three days until the pursuers have returned. Then afterward you may go your way."¹⁷The men said to her, "We will be guiltless with respect to this oath of yours that you have made us swear.¹⁸Behold, when we come into the land, you shall tie this scarlet cord in the window through which you let us down,and you shall gather into your house your father and mother, your brothers, and all your father's household.¹⁹Then if anyone goes out of the doors of your house into the street,his blood shall be on his own head, and we shall be guiltless. But if a hand is laid on anyone who is with you in the house, his blood shall be on our head.²⁰But if youtell this business of ours, then we shall be guiltless with respect to your oath that you have made us swear."²¹And she said, "According to your words, so be it." Then she sent them away, and they departed. And she tied the scarlet cord in the window.

²²They departed and went into the hills and remained there three days until the pursuers returned, and the pursuers searched all along the way and found nothing.²³Then the two men returned. They came down from the hills andpassed over and came to Joshua the son of Nun, and they told him all that had happened to them.²⁴And they said to Joshua, "TrulytheLordhas given all the land into our hands. And also, all the inhabitants of the landmelt away because of us."

Now the word of theLordcame toJonah the son of Amittai, saying,²"Arise, go toNineveh, thatgreat city, and call out against it,for their evilhas come up before me."³But Jonahrose to flee toTarshish from the presence of theLord. He went down toJoppa and found a ship going toTarshish. So he paid the fare and went down into it, to go with them toTarshish,away from the presence of theLord.

⁴ButtheLordhurled a great wind upon the sea, and there was a mighty tempest on the sea, so that the ship threatenedto break up.⁵Then the mariners were afraid, andeach cried out to his god. Andthey hurled the cargo that was in the ship into the sea to lighten it for them. But Jonah had gone down into the inner part of the ship and had lain down and was fast asleep.⁶So the captain came and said to him, "What do you mean, you sleeper? Arise,call out to your god!Perhaps the god will give a thought to us, that we may not perish."

⁷And they said to one another, "Come, let uscast lots, that we may know on whose account this evil has come upon us." So they cast lots, and the lot fell on Jonah.⁸Then they said to him, "Tell us on whose account this evil has come upon us. What is your occupation? And where do you come from? What is your country? And of what people are you?"⁹And he said to them, "I am a Hebrew, and I feartheLord, the God of heaven,who made the sea and the dry land."¹⁰Then the men were exceedingly afraid and said to him, "What is this that you have done!" For the men knew thathe was fleeing from the presence of theLord, because he had told them.

¹¹Then they said to him, "What shall we do to you, that the sea may quiet down for us?" For the sea grew more and more tempestuous.¹²He said to them, "Pick me up and hurl me into the sea; then the sea will quiet down for you,for I know it is because of me that this great tempest has come upon you."¹³Nevertheless, the men rowed hardto get back to dry land, but they could not, for the sea grew more and more tempestuous against them.¹⁴Therefore they called out to theLord, "OLord, let us not perish for this man's life, andlay not on us innocent blood,for you, OLord, have done as it pleased you."¹⁵So they picked up Jonah and hurled him into the sea,and the sea ceased from its raging.¹⁶Then the men feared theLordexceedingly,and they offered a sacrifice to theLordand made vows.

¹⁷And theLordappointeda great fish to swallow up Jonah.And Jonah was in the belly of the fish three days and three nights.

Then Jonah prayed to theLordhis God from the belly of the fish,²saying,

"I called out to theLord, out of my distress, and he answered me; out of the belly of Sheol I cried, and you heard my voice. ³For you cast me into the deep, into the heart of the seas, and the flood surrounded me; all your waves and your billows passed over me. ⁴Then I said, 'I am driven away from your sight; yet I shall again look upon your holy temple.' ⁵The waters closed in over meto take my life; the deep surrounded me; weeds were wrapped about my head ⁶ at the roots of the mountains. I went down to the land whose bars closed upon me forever; yet you brought up my life from the pit, OLordmy God. ⁷When my life was fainting away, I remembered theLord, and my prayer came to you, into your holy temple. ⁸Those who pay regard to vain idols forsake their hope of steadfast love. ⁹But I with the voice of thanksgiving will sacrifice to you; what I have vowed I will pay. Salvation belongs to theLord!"

¹⁰And theLordspoke to the fish, and it vomited Jonah out upon the dry land.

Then the word of theLordcame to Jonah the second time, saying,²"Arise, go toNineveh, that great city, and call out against it the message that I tell you."³So Jonah arose and went to Nineveh, according to the word of theLord. NowNineveh was an exceedingly great city,three days' journey in breadth.⁴Jonah began to go into the city, going a day's journey. And he called out, "Yet forty days, and Nineveh shall be overthrown!"⁵And the people of Nineveh believed God.They called for a fast andput on sackcloth, from the greatest of them to the least of them.

⁶The word reachedthe king of Nineveh, andhe arose from his throne, removed his robe, covered himself with sackcloth,and sat in ashes.⁷And he issued a proclamation and published through Nineveh,"By the decree of the king and his nobles: Let neither man norbeast, herd nor flock, taste anything. Let them not feed or drink water,⁸but let man andbeast be covered with sackcloth, and let them call out mightily to God.Let everyone turn from his evil way and fromthe violence that is in his hands.⁹Who knows? God may turn and relentand turn from his fierce anger, so that we may not perish."

¹⁰When God saw what they did,how they turned from their evil way,God relented of the disaster that he had said he would do to them, and he did not do it.

Paul and Timothy, servantsof Christ Jesus,

To all thesaints in Christ Jesus who are at Philippi, with theoverseersanddeacons:

²Grace to you and peace from God our Father and the Lord Jesus Christ.

³I thank my Godin all my remembrance of you,⁴always in every prayer of mine for you all making my prayer with joy,⁵because of your partnership in the gospel from the first day until now.⁶And I am sure of this, that he who begana good work in youwill bring it to completion atthe day of Jesus Christ.⁷It is right for me to feel this way about you all, because I hold youin my heart, for you are allpartakers with me of grace,bothin my imprisonment and inthe defense and confirmation of the gospel.⁸ForGod is my witness,how I yearn for you all with the affection of Christ Jesus.⁹And it is my prayer thatyour love may abound more and more,with knowledge and all discernment,¹⁰so that you may approve what is excellent,and so be pure and blamelessfor the day of Christ,¹¹filledwith the fruit of righteousness that comesthrough Jesus Christ,to the glory and praise of God.

¹²I want you to know, brothers,that what has happened to me has reallyserved to advance the gospel,¹³so that it has become known throughout the whole imperial guardandto all the rest thatmy imprisonment is for Christ.¹⁴And most of the brothers, having become confident in the Lord by my imprisonment, are much more boldto speak the wordwithout fear.

¹⁵Some indeed preach Christ from envy and rivalry, but others from good will.¹⁶The latter do it out of love,knowing that I am put here forthe defense of the gospel.¹⁷The former proclaim Christout of selfish ambition, not sincerely but thinking to afflict me in my imprisonment.¹⁸What then? Only that in every way, whether in pretense or in truth, Christ is proclaimed, and in that I rejoice.

Yes, and I will rejoice,¹⁹for I know thatthrough your prayers andthe help ofthe Spirit of Jesus Christ this will turn out for my deliverance,²⁰as it is my eager expectation and hopethat I will not be at all ashamed, but that with fullcourage now as always Christwill be honored in my body,whether by life or by death.²¹For to meto live is Christ, and to die is gain.²²If I am to live in the flesh, that means fruitful labor for me. Yet which I shall choose I cannot tell.²³I am hard pressed between the two. My desire isto depart andbe with Christ, for that is far better.²⁴But to remain in the flesh is more necessary on your account.²⁵Convinced of this,I know that I will remain and continue with you all, for yourprogress andjoy in the faith,²⁶so that in meyou may have ample cause to glory in Christ Jesus, because of my coming to you again.

²⁷Onlylet your manner of life beworthyof the gospel of Christ, so that whether I come and see you or am absent, I may hear of youthat you are standing firm in one spirit, withone mindstriving side by side for the faith of the gospel,²⁸and not frightened in anything by your opponents. This isa clear sign to them of their destruction, butof your salvation, and that from God.²⁹Forit has been granted to you that for the sake of Christ you should not only believe in him but alsosuffer for his sake,³⁰engaged in the sameconflict thatyou saw I had and now hear that I still have.

So if there is any encouragement in Christ, any comfort fromlove, anyparticipation in the Spirit, anyaffection and sympathy,²complete my joy by beingof the same mind, having the same love, being in full accord and of one mind.³Do nothing fromselfish ambition orconceit, but inhumility count others more significant than yourselves.⁴Let each of youlook not only to his own interests, but also to the interests of others.⁵Have this mind among yourselves, which is yours in Christ Jesus,⁶who, though he was inthe form of God, did not count equality with Goda thing to be grasped,⁷butemptied himself, by taking the form of aservant,being born in the likeness of men.⁸And being found in human form, he humbled himself bybecoming obedient to the point of death,even death on a cross.⁹ThereforeGod hashighly exalted him and bestowed on himthe name that is above every name,¹⁰so that at the name of Jesusevery knee should bow,in heaven and on earth and under the earth,¹¹andevery tongue confess that Jesus Christ isLord, to the glory of God the Father.

¹²Therefore, my beloved,as you have alwaysobeyed, so now, not only as in my presence but much more in my absence, work out your own salvation with fear and trembling,¹³forit is God who works in you, both to will and to work forhis good pleasure.

¹⁴Do all thingswithout grumbling ordisputing,¹⁵that you may be blameless and innocent,children of Godwithout blemishin the midst ofa crooked and twisted generation, among whom you shineas lights in the world,¹⁶holding fast tothe word of life, so that inthe day of ChristI may be proud thatI did not run in vain or labor in vain.¹⁷Even if I am to bepoured out as a drink offering uponthe sacrificial offering of your faith, I am glad and rejoice with you all.¹⁸Likewise you also should be glad and rejoice with me.

¹⁹I hope in the Lord Jesusto send Timothy to you soon, so that I too may be cheered by news of you.²⁰For I have no onelike him, who will be genuinely concerned for your welfare.²¹For they allseek their own interests, not those of Jesus Christ.²²But you know Timothy'sproven worth, howas a sonwith a fatherhe has served with me in the gospel.²³I hope therefore to send him just as soon as I see how it will go with me,²⁴andI trust in the Lord that shortly I myself will come also.

²⁵I have thought it necessary to send to youEpaphroditus my brother and fellow worker andfellow soldier, and your messenger andminister to my need,²⁶for he has been longing for you all and has been distressed because you heard that he was ill.²⁷Indeed he was ill, near to death. But God had mercy on him, and not only on him but on me also, lest I should have sorrow upon sorrow.²⁸I am the more eager to send him, therefore, that you may rejoice at seeing him again, and that I may be less anxious.²⁹Soreceive him in the Lord with all joy, andhonor such men,³⁰for he nearly diedfor the work of Christ, risking his lifeto complete what was lacking in your service to me.

Finally, my brothers,rejoice in the Lord.To write the same things to you is no trouble to me and is safe for you.

²Look out forthe dogs, look out forthe evildoers, look out for those who mutilate the flesh.³Forwe are the circumcision,who worshipby the Spirit of Godandglory in Christ Jesus and put no confidence in the flesh⁴though I myself have reason for confidence in the flesh also. If anyone else thinks he has reason for confidence in the flesh, I have more:⁵circumcised on the eighth day,of the people of Israel,of the tribe of Benjamin,a Hebrew of Hebrews; as to the law,a Pharisee;⁶as to zeal,a persecutor of the church;as to righteousness under the law,blameless.⁷Butwhatever gain I had,I counted as loss for the sake of Christ.⁸Indeed, I count everything as loss because ofthe surpassing worth ofknowing Christ Jesus my Lord. For his sake Ihave suffered the loss of all things and count them as rubbish, in order that I may gain Christ⁹and be found in him, not havinga righteousness of my own that comes from the law, butthat which comes through faith in Christ, the righteousness from God that depends on faith¹⁰that I may know him andthe power of his resurrection, andmay share his sufferings, becoming like him in his death,¹¹that by any means possible I mayattain the resurrection from the dead.

¹²Not that I have alreadyobtained this oram already perfect, but I press on to make it my own, because Christ Jesus has made me his own.¹³Brothers, I do not consider that I have made it my own. But one thing I do:forgetting what lies behind and straining forward to what lies ahead,¹⁴I press on toward the goal forthe prize of the upwardcall of God in Christ Jesus.¹⁵Let those of us who aremature think this way, and if in anythingyou think otherwise,God will reveal that also to you.¹⁶Onlylet us hold true to what we have attained.

¹⁷Brothers,join in imitating me, and keep your eyes on those who walkaccording to the example you have in us.¹⁸Formany, of whom I have often told you and now tell youeven with tears, walk as enemies of the cross of Christ.¹⁹Their end is destruction,their god is their belly, andthey glory in their shame, withminds set on earthly things.²⁰Butour citizenship is in heaven, andfrom it weawait a Savior, the Lord Jesus Christ,²¹who will transformour lowly bodyto be like his glorious body,by the power that enables him evento subject all things to himself.