GlenCalc

Z-score calculator

A z-score says how many standard deviations a value is from the mean. Enter the value and the distribution to get its z-score and percentile.

Your answer

z-score1.5
Percentile93.3193 %
P(X < value)0.933193
P(X > value)0.066807
P(−|z| < Z < |z|)0.866386

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How we worked it out

Updated as you change the numbers.

  1. z = (x − mean) ÷ SD = (85 − 70) ÷ 10.
  2. The percentile is the area under the standard normal curve to the left of z.

Method and assumptions

z = (x − μ) ÷ σ. Probabilities come from the standard normal cumulative distribution, computed with a high-accuracy error-function series rather than a printed table. This assumes the data are normally distributed.

Questions

What is the z-score of 85 if the mean is 70 and the SD is 10?

1.5, the 93.32nd percentile.

Sources

Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.

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