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# DigitalWater.r
# Statypus Water: Digital Production Audit
# Course Resources: statypus.org
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# 1. SET MACHINE PARAMETERS
mu    <- 500.5
sigma <- 0.2

# 2. PHASE 1: THE LONE WOLF (n=1)
# Generate 10,000 individual bottles.
lone_wolves <- rnorm(10000, mean = mu, sd = sigma)

# Plot with 0.3mL Target Zone goalposts (Red dashed lines)
hist(lone_wolves, main = "Individual Bottles (n=1)",
     xlim = c(499.5, 501.5), col = "gray90", border = "white")
abline(v = c(500.2, 500.8), col = "red", lwd = 3, lty = 2)

# Proportion Check: How many fell outside the Target Zone (500.2 to 500.8)?
mean(lone_wolves < 500.2 | lone_wolves > 500.8)


# 3. PHASE 3: THE SNIPER RIFLE (10,000 Cases of n=16)
# Simulating 10,000 unique cases (16 bottles each).
# Storing the average volume of each case in 'case_avgs'.
case_avgs <- replicate(10000, mean(rnorm(16, mean = mu, sd = sigma)))

# Plot the averages (Using skyblue for on-screen clarity)
hist(case_avgs, main = "10,000 Case Averages (n=16)",
     xlim = c(499.5, 501.5), col = "skyblue", border = "white")
abline(v = c(500.2, 500.8), col = "red", lwd = 3, lty = 2)


# 4. THE AUDIT
# Out of our 10,000 simulated cases, how many hit the mark of 500.1 or less?
sum(case_avgs <= 500.1)