What does a z-score of 2 mean?

A z-score of 2 means the value is 2 standard deviations above the mean. In a normal distribution that corresponds to roughly the 97.7th percentile, a relatively high but not extreme value.

What's the difference between one-tailed and two-tailed p-values?

The one-tailed p-value is the probability of a value at least this extreme in one direction. The two-tailed p-value doubles that, covering extremes in either direction, and is typically used when you don't have a directional hypothesis before testing.

Z-Score & P-Value Calculator

Calculate a z-score, percentile, and p-value from a value, mean and standard deviation.

How this is calculated

z = (x − μ) ÷ σ; p-value derived from the standard normal CDF of z

Assumptions used in this calculation

Normal distribution: Assumes the underlying data is normally distributed.

About this calculator

Calculates the z-score for a value relative to a mean and standard deviation, along with its percentile and one/two-tailed p-values, consolidating the master prompt's separate 'Z-Score Calculator' and 'P-Value Calculator', since the p-value is derived directly from the z-score.

Worked example

Value 85, mean 75, sd 5

Result: Z-score = 2, percentile ≈ 97.7%, p (one-tailed) ≈ 0.0228

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Z-Score & P-Value Calculator

About this calculator

Frequently asked questions

What does a z-score of 2 mean?

What's the difference between one-tailed and two-tailed p-values?

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