This phrase came from the book Understanding Probability written by Henk Tijms. The original sentence is:
the probability that a normally distributed random variable will take on a value that lies z or more standard deviations above the expected value is equal to 1 − Φ(z) for z > 0, as is the probability of a value that lies z or more standard deviations below the expected value.
I don't understand what lies means in this context. I have checked The Oxford Advanced Learner's Dictionary, and Webster's online; none of their explanations refer lie as a transitive verb. How can it used with z or more standard deviations, which is obviously a noun phrase?
Could anyone explain to me:
- What does the sentence mean?
- The grammar underlying this sentence? Am I right that the lie used here is actually a transitive verb?