FTA Calculator: engineering calculator for fta. Formula derivation, tolerances, and design tips.
Mean: x̄ = Σxᵢ / n
Sample standard deviation: s = √[Σ(xᵢ − x̄)² / (n − 1)] — the (n−1) denominator gives an unbiased estimate of population variance from a sample.
Z-score (standard score): z = (x − μ) / σ — transforms a raw value into the number of standard deviations it lies from the mean.
95% Confidence interval for a mean: x̄ ± 1.96 × (s / √n) — gives the range within which the true population mean lies with 95% confidence, assuming normality.
Worked example: n=50 students, mean score 72, SD 12. 95% CI = 72 ± 1.96 × (12/√50) = 72 ± 3.33 → [68.67, 75.33].