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1) A normal random variable is fully determined by its mean μ only.
2) Standardizing uses the formula z = (x − μ) / σ^2.
3) For any normal distribution, P(X > μ) = 0.5.
4) Approximately 50% of a normal distribution lies within μ ± 1σ.
5) For the standard normal Z ~ N(0,1), Φ(0) = 0.5.
6) In Excel, NORM.DIST(x, μ, σ, TRUE) returns the PDF value at x.
7) NORM.S.INV(0.975) ≈ 1.96 (the 97.5th percentile of the standard normal).
8) If the standard deviation doubles (σ → 2σ), the z-score for a fixed x increases in magnitude.
9) For a normal distribution, the median equals the mean.
10) For any continuous distribution, including normal, P(X = a) = 0.
11) If X ~ N(μ, σ²) and a, b are constants (a ≠ 0), then aX + b is also normally distributed.
12) If X ~ N(μ, σ²) then Z = (X − μ)/σ follows N(0,1).
13) The normal distribution is memoryless.
14) A 68% central interval for X ~ N(μ, σ²) is [μ − 1.96σ, μ + 1.96σ].
15) In Excel, NORM.INV(p, μ, σ) returns the value x such that P(X ≤ x) = p for X ~ N(μ, σ²).