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Z-Score Calculator
Convert raw scores to z-scores and read off normal distribution probabilities, including left-tail, right-tail, and two-tailed p-values from z.
From raw score x
This treats x as a value from a normal distribution N(mu, sigma^2) and computes its z-score and probabilities.
z score calculatorp-value from z (two-tailed)
Results
z-score
1.96
P(X <= x) (left-tail)
0.975002
P(X >= x) (right-tail)
0.024998
Two-tailed p-value for |z|
0.049996
From z-score
Use this for quick normal distribution look-ups like z = 1.96 or z = -2.5.
Standard normal probabilities
P(Z <= z)
0.975002
P(Z >= z)
0.024998
Two-tailed p-value
0.049996
How to use this tool
- Enter a mean, standard deviation, and raw score x to compute its z-score.
- Read off left-tail, right-tail, and two-tailed probabilities from the normal distribution.
- Alternatively, enter a z value directly to convert z scores to p-values.
Z score calculator for p-values
- Quickly convert between raw scores and z-scores for a normal distribution.
- Use the two-tailed probability to match typical hypothesis test p-values.
- Ideal as a replacement for printed z tables in stats courses.
What this normal distribution calculator assumes
- The underlying variable is approximately normally distributed with mean mu and standard deviation sigma.
- Probabilities are computed using a high-quality approximation to the standard normal CDF.
- Results are rounded for readability but retain enough precision for most homework and exam questions.
FAQ
- Is this the same as using a z table?
- Yes. This z score calculator automates the same standard normal lookup you would do with a printed z table, but gives you left, right, and two-tailed probabilities instantly.
- Can I use this for p-values in hypothesis tests?
- Yes. Enter your test statistic as a z-score or compute it via mu, sigma, and x, then use the two-tailed probability as the p-value for a two-sided z test.
- Does it support t-distributions?
- This tool focuses on the normal distribution and z-scores. For small samples or unknown variance, you would typically use a t-distribution instead.
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