📊 Z-Table

standard normal distribution · Φ(z) = P(Z ≤ z) · cumulative left-tail probabilities

🔢 Z-Score Calculator

Left tail
—
Φ(z) = P(Z ≤ z)
Right tail
—
P(Z > z)
Two-tail
—
P(|Z| ≤ |z|)
Φ(z) = P(Z ≤ z) — cumulative from −∞ to z
1 − Φ(z) = P(Z > z) — right tail
2Φ(|z|) − 1 = P(−|z| ≤ Z ≤ |z|) — central area
Φ(−z) = 1 − Φ(z) — symmetry of normal dist.

🔔 Bell Curve

Shaded area = Φ(z)

🔄 Inverse Lookup

→ z = —
Enter a cumulative probability to find its z-score

📋 Standard Normal Table

Click any cell to load that z-score into the calculator above · rows = ones & tenths · columns = hundredths
What is this?

The Z-Table shows the probability that a value falls below a given z-score in a standard normal distribution — the symmetric bell curve centred at zero with standard deviation of one.

Why does it matter?

The Z-Table is used in statistics, psychology, biology, and standardized testing (SAT, GRE) to calculate percentiles, compare datasets, and test scientific hypotheses.

Key terms
Z-score — how many standard deviations a value is from the mean: z = (x − μ) / σ Standard deviation (σ) — measures how spread out data is around the mean Normal distribution — a symmetric, bell-shaped distribution of data around its mean Percentile — the percentage of data values falling below a given point Mean (μ) — the centre of the distribution where data clusters most densely
🎯 Try this challenge

What percentage of data in a normal distribution falls within 1 standard deviation of the mean? Look up z = 1.00 and z = −1.00 in the table, then calculate the area between them.

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