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📈 Z-Score & Normal Distribution 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.
Normal Distribution & Z‑Score Calculator
Convert raw scores to z‑scores, and read off left‑tail, right‑tail, and two‑tailed probabilities from the standard normal distribution. Ideal for stats classes and quick p‑value checks.
From raw score x
Mean (μ)
Standard deviation (σ > 0)
Value (x)
This treats x as a value from a normal distribution N(μ, σ²) 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
z
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 μ and standard deviation σ.
- 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 μ, σ, 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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