Tools

Z-Score / Normal Distribution Calculator

Enter an observation with the mean and standard deviation of its population. Gives the Z-score, where it lands on the bell curve, its percentile rank, the tail probabilities either side of it, and how rare a reading that far out actually is.

Z-Score

+1.0000

70 is 1.00σ above a mean of 60

Where It Lands (shaded area = P(X < 70) = 84.13%)

-3σ-2σ-1σ+1σ+2σ+3σx = 70
below x the observation

Percentile

84.13%

of the population is lower

P(X < x)

0.841345

left tail

P(X > x)

0.158655

right tail

Rarity

1 in 3

this far out, either side

Reading

Between 1 and 2 standard deviations from the mean

-3σ

30

-2σ

40

-1σ

50

60

+1σ

70

+2σ

80

+3σ

90

The highlighted band is the σ step your value rounds to.

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