Exercise 1: A Latency Probability, Estimated and Then Computed Precisely — Possible Solution
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GIVEN
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mu = 150ms, sigma = 20ms, x = 110ms

STEP 1: THE Z-SCORE
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z = (x - mu) / sigma = (110 - 150) / 20 = -40/20 = -2

STEP 2: THE EMPIRICAL RULE ESTIMATE
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Per this chapter's own empirical rule, about 95% of values fall within
2 standard deviations of the mean, leaving about 5% outside that
range, split evenly between the two tails - about 2.5% below -2
standard deviations (110ms) and about 2.5% above +2 standard
deviations (190ms).

Empirical rule estimate: P(X < 110ms) ~= 2.5%

STEP 3: THE PRECISE VALUE
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Using the standard normal CDF at z = -2:

  P(X < 110ms) = standard_normal_cdf(-2) ~= 0.02275 (2.275%)

STEP 4: COMPARING THE TWO
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The empirical rule's quick estimate (2.5%) and the precise calculation
(2.275%) are close, differing by only about a quarter of a percentage
point - exactly the same small gap this chapter's own worked response-
time example showed at the equivalent z=2 point. The empirical rule is
a genuinely useful fast approximation, not merely a rough guess.

WHY THIS WORKS AS AN ANSWER
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The z-score is computed directly from this chapter's own formula, the
empirical rule is applied correctly by recognizing 110ms sits exactly
2 standard deviations below the mean, and the precise value is
computed via the standard normal CDF and explicitly compared back to
the estimate rather than reported in isolation.