Normal Distribution
Review
z-score: how many standard
deviations the point is from
the mean.
Probability
Example:
𝑁~(66.4, 31.36)
70 𝑘𝑔: 𝑧 =
70 − 66.4
= 0.6429
5.6
𝑃(X ≤ 70)= 0.7389 + 0.0010 = 0.7399
72.5 𝑘𝑔: 𝑧 =
72.5 − 66.4
= 1.089
5.6
𝑃 𝑥 ≤ 72.5 = 0.8599 + 0.0021 = 0.8620
𝑃 70 ≤ 𝑥 ≤ 72.5 = 0.8620 − 0.7399 = 0.1221
.1221 × 250 = 30.525
About 30 sheep
Working Backwards:
𝑁~(𝜇, 24.21)
Find z-score
𝑧 = 0.674
𝑧=
67.5 − 𝜇
= 0.674
4.92
𝜇 = 64.2
• Use this to get probabilities that would
take a long time to calculate using the
binomial formula
• If the problem says “approximate”
• 𝑛𝑝 > 5 𝑎𝑛𝑑 𝑛𝑞 > 5
• Apply continuity correction