"All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work." (2 Timothy 3:16-17, NKJV)

Strictly speaking, only the "autographs" (the original documents penned by the Biblical authors) are inspired. Copies of the original documents are virtually inspired to the extent that they accurately reflect the original documents. 

The evidence -- bibliographical, historical, and archaeological -- indicates that that they do accurately reflect the original documents!   For example, Homer's Iliad ranks second (643 copies) to the New Testament (24,000+) in possessing the greatest amount of ancient manuscript testimony. Let's compare^* them:
 

Applying textual analysis to all existing early manuscripts:
 

Of the ½% New Testament variant readings, most involve nothing more than a missing letter in a word, a misspelling, or a reversal of the order of two words. Of the others, not one essential point of Christian doctrine rests upon a disputed reading. A similar comparison of Old Testament books to other ancient texts^* is similarly conclusive. 

Unlike any ancient text in existence, God has definitely guided the hands of the men He entrusted to bring us His Scriptures!

Sources/ To learn more: 

1. Harris, Glenn. Can I Trust the Bible? 
2. ^*McDowell, Josh. (1972) Evidence that Demands a Verdict. Campus Crusade.
3. Perman, Matt. Historical Evidence for the Bible 
4. Ross, High. Fulfilled Prophecy: Evidence for the Reliability of the Bible