Exercise 1: Standard Error and a Z-Score for a Users Metric — Possible Solution
====================================================================

GIVEN
------------------------------
sigma = 200 users, n = 25 days
Sample mean is 90 users above the assumed population mean.

STEP 1: THE STANDARD ERROR
------------------------------
SE = sigma / sqrt(n) = 200 / sqrt(25) = 200 / 5 = 40

STEP 2: THE Z-SCORE
------------------------------
z = (sample mean - assumed population mean) / SE
  = 90 / 40
  = 2.25

STEP 3: INTERPRETING THE RESULT
------------------------------
A z-score of 2.25 means the observed sample mean sits more than 2
standard errors away from the assumed population mean. Per this
chapter's own worked example (where a z-score of 0.667 was called
"thoroughly unremarkable, well within a single standard error"), a
z-score this much larger - over 2 - is NOT unremarkable. It's a
notably large deviation, the kind of result that starts to suggest
something may genuinely differ from the assumed population mean,
rather than being explainable purely by ordinary sampling error alone
(though this chapter doesn't yet provide the formal tool - hypothesis
testing, Chapter 4 - to make that determination with real
statistical rigor).

WHY THIS WORKS AS AN ANSWER
------------------------------
The standard error and z-score are computed directly using this
chapter's own formulas, and the interpretation is grounded in a direct
comparison against this chapter's own worked example's much smaller
z-score, rather than judging "large" or "small" without a concrete
point of reference.