See here for more on Miranda's story and Miranda v. Arizona.

"Beyond a reasonable doubt" can be a confusing standard because it is not as simple to conceive as the "more likely than not" or "greater than a 50% likelihood" that exists with the "preponderance of the evidence" standard.

A reasonable doubt is a doubt for which a reason can be given, based on common sense and a fair and rational consideration of the evidence. A doubt based on guesswork or speculation is not a reasonable doubt.

See Wisconsin Criminal Jury Instruction 140.

In other words, based on common sense and a rational consideration of the evidence, the weight of the credible evidence in favor of the plaintiff's claims is greater than the evidence opposed to the plaintiff's claims.

See Wisconsin Civil Jury Instruction 200.