Use this as a step‑by‑step walkthrough in class. The examples below use hypothetical Statics grade dataset (n = 150) with sample statistics \(\mu \approx 83.54\) and \(\sigma \approx 7.44\) (sample stdev).
Assume grades are in B2:B151.
| Measure | Excel Formula | Meaning | 
|---|---|---|
| Mean (\(\mu\)) | =AVERAGE(B2:B151) | Center of the distribution | 
| Standard Deviation (\(\sigma\)) | =STDEV.S(B2:B151) | Spread of the grades (use STDEV.S for a sample) | 
| Min / Max | =MIN(B2:B151) / =MAX(B2:B151) | Range check | 
| Count | =COUNT(B2:B151) | Sample size | 
For our dataset: \(n=150\), \(\mu\approx83.54\), \(\sigma\approx7.44\), min = 69, max = 100.
Standardize any grade \(x\) to a z‑score:
Excel (if mean in D2 and stdev in D3): =(B2-$D$2)/$D$3
| Task | Excel Formula | Math Equivalent | 
|---|---|---|
| Left‑tail \(P(X\le x)\) | =NORM.DIST(x, μ, σ, TRUE) | \(F(x)\) | 
| Right‑tail \(P(X\ge x)\) | =1-NORM.DIST(x, μ, σ, TRUE) | \(1-F(x)\) | 
| Between \(P(a\le X\le b)\) | =NORM.DIST(b, μ, σ, TRUE)-NORM.DIST(a, μ, σ, TRUE) | \(F(b)-F(a)\) | 
| Percentile → x | =NORM.INV(p, μ, σ) | solve \(x=\mu+\sigma z_p\) | 
The z‑score transforms any normal random variable \(X\sim\mathcal{N}(μ,σ^2)\) into the standard normal \(Z\sim\mathcal{N}(0,1)\):
This rescaling centers the distribution at 0 and makes the spread 1. Historically, before computers, students used printed z‑tables to look up \(Φ(z)=P(Z≤z)\) and find probabilities. Today, Excel and calculators compute \(P(X≤x)\) directly, but z‑scores are still crucial for:
Bottom line: Excel doesn’t require you to compute z to get probabilities, but learning z builds conceptual understanding and prepares students for hypothesis testing and theoretical statistics.
Mean: =AVERAGE(B2:B151)
Stdev (sample): =STDEV.S(B2:B151)
Left tail P(X≤x): =NORM.DIST(x, $D$2, $D$3, TRUE)
Right tail P(X≥x): =1-NORM.DIST(x, $D$2, $D$3, TRUE)
Between a..b: =NORM.DIST(b,$D$2,$D$3,TRUE)-NORM.DIST(a,$D$2,$D$3,TRUE)
Percentile → x: =NORM.INV(p, $D$2, $D$3)
z-score for cell B2: =(B2-$D$2)/$D$3
    Replace x, a, b, and p with your chosen values. Cells D2 and D3 hold the computed mean and stdev.
| student id | Statics_Grade | 
|---|---|
| 1 | 75 | 
| 2 | 71 | 
| 3 | 74 | 
| 4 | 90 | 
| 5 | 74 | 
| 6 | 100 | 
| 7 | 86 | 
| 8 | 83 | 
| 9 | 75 | 
| 10 | 88 | 
| 11 | 77 | 
| 12 | 83 | 
| 13 | 100 | 
| 14 | 81 | 
| 15 | 91 | 
| 16 | 76 | 
| 17 | 82 | 
| 18 | 96 | 
| 19 | 77 | 
| 20 | 96 | 
| 21 | 88 | 
| 22 | 78 | 
| 23 | 87 | 
| 24 | 90 | 
| 25 | 87 | 
| 26 | 69 | 
| 27 | 76 | 
| 28 | 80 | 
| 29 | 81 | 
| 30 | 87 | 
| 31 | 83 | 
| 32 | 71 | 
| 33 | 85 | 
| 34 | 87 | 
| 35 | 86 | 
| 36 | 91 | 
| 37 | 89 | 
| 38 | 86 | 
| 39 | 81 | 
| 40 | 69 | 
| 41 | 85 | 
| 42 | 84 | 
| 43 | 84 | 
| 44 | 72 | 
| 45 | 73 | 
| 46 | 90 | 
| 47 | 82 | 
| 48 | 87 | 
| 49 | 82 | 
| 50 | 82 | 
| 51 | 90 | 
| 52 | 78 | 
| 53 | 83 | 
| 54 | 78 | 
| 55 | 79 | 
| 56 | 80 | 
| 57 | 84 | 
| 58 | 78 | 
| 59 | 92 | 
| 60 | 75 | 
| 61 | 81 | 
| 62 | 78 | 
| 63 | 94 | 
| 64 | 84 | 
| 65 | 90 | 
| 66 | 70 | 
| 67 | 84 | 
| 68 | 89 | 
| 69 | 83 | 
| 70 | 91 | 
| 71 | 78 | 
| 72 | 93 | 
| 73 | 100 | 
| 74 | 79 | 
| 75 | 78 | 
| 76 | 94 | 
| 77 | 95 | 
| 78 | 78 | 
| 79 | 79 | 
| 80 | 80 | 
| 81 | 71 | 
| 82 | 75 | 
| 83 | 74 | 
| 84 | 76 | 
| 85 | 82 | 
| 86 | 84 | 
| 87 | 94 | 
| 88 | 74 | 
| 89 | 90 | 
| 90 | 80 | 
| 91 | 82 | 
| 92 | 87 | 
| 93 | 73 | 
| 94 | 85 | 
| 95 | 83 | 
| 96 | 86 | 
| 97 | 84 | 
| 98 | 100 | 
| 99 | 77 | 
| 100 | 78 | 
| 101 | 77 | 
| 102 | 78 | 
| 103 | 77 | 
| 104 | 92 | 
| 105 | 93 | 
| 106 | 77 | 
| 107 | 75 | 
| 108 | 86 | 
| 109 | 78 | 
| 110 | 87 | 
| 111 | 84 | 
| 112 | 70 | 
| 113 | 94 | 
| 114 | 96 | 
| 115 | 77 | 
| 116 | 79 | 
| 117 | 84 | 
| 118 | 85 | 
| 119 | 87 | 
| 120 | 98 | 
| 121 | 81 | 
| 122 | 76 | 
| 123 | 71 | 
| 124 | 76 | 
| 125 | 82 | 
| 126 | 96 | 
| 127 | 78 | 
| 128 | 84 | 
| 129 | 82 | 
| 130 | 92 | 
| 131 | 100 | 
| 132 | 78 | 
| 133 | 78 | 
| 134 | 90 | 
| 135 | 87 | 
| 136 | 97 | 
| 137 | 87 | 
| 138 | 79 | 
| 139 | 87 | 
| 140 | 91 | 
| 141 | 89 | 
| 142 | 86 | 
| 143 | 91 | 
| 144 | 91 | 
| 145 | 93 | 
| 146 | 87 | 
| 147 | 81 | 
| 148 | 83 | 
| 149 | 92 | 
| 150 | 75 | 
Enter your dataset’s mean (μ) and stdev (σ), or click “Use practice dataset”. Once μ and σ are known, the entire distribution is defined — no need to reference every data point!
| Mean (μ) | |
| Stdev (σ) | 
| x | |
| z = (x−μ)/σ | |
| P(X ≤ x) | 
| p (0–1) | |
| zp = Φ⁻¹(p) | |
| x = μ + σ·zp | 
| a | |
| b | |
| P(a ≤ X ≤ b) | 
Excel equivalents: NORM.DIST(x, μ, σ, TRUE), 1−NORM.DIST(x, μ, σ, TRUE), NORM.DIST(b, μ, σ, TRUE)−NORM.DIST(a, μ, σ, TRUE), NORM.INV(p, μ, σ).