130 is 2.000 standard deviations above the mean. About 97.72% of values fall below it.
| z = (x − μ) / σ | 2.000000 |
| Percentile, P(Z ≤ z) × 100 | 97.7250% |
| Left tail, P(Z ≤ z) | 0.977250 |
| Right tail, P(Z ≥ z) | 0.022750 |
| Two-tailed, P(|Z| ≥ |z|) | 0.045500 |
A value at the 97.5th percentile has z = 1.959964. Check: Φ(z) × 100 = 97.500000.
Uses the mean and standard deviation entered above.
z from -1.0000 to 1.0000. P(85 < X < 115) = Φ(zhi) − Φ(zlo) = 0.682689, or 68.27%.
Φ is the standard normal cumulative distribution. Values use the regularized incomplete gamma function, checked in the test suite against published tables to within 10⁻⁹.
Find the z score, percentile and p-value for any value. A z score says how many standard deviations a value sits above or below the mean: z = (x − μ) / σ. If the data are roughly normal, the z score also gives the percentile and the probability in each tail. This calculator takes a value, mean and standard deviation and returns the z score, the percentile, the left and right tail probabilities, and the two-tailed p-value. It also runs the other way, from a percentile to a z score.
The z score puts values from different scales on one scale. Once you have z, a table or this calculator converts it into a probability with the standard normal distribution. 100% free, no registration, and complete privacy — everything runs locally in your browser, so your data never touches a server.
Enter the three numbers and the calculator returns z = (x − μ) / σ, rounded to six decimal places in the result table.
Get the percentile, the left tail P(Z ≤ z), the right tail P(Z ≥ z) and the two-tailed P(|Z| ≥ |z|) in one table.
Enter a percentile and get the z score that corresponds to it, with a check value that recomputes the percentile.
The normal CDF uses the regularized incomplete gamma function and is checked against published reference values. Nothing you enter leaves the page.
Confidence intervals for a mean (z or t) and for a proportion.
Shuffle a list into balanced random groups.
Standard normal probabilities and critical z values to four decimals.
One-tailed and two-tailed p-values for a z or t test statistic.
Event probability, complements, P(A or B) and conditional probability.
Least-squares slope, intercept and the slope test.
It means the value is 1.96 standard deviations above the mean. About 97.5% of a normal distribution lies below that point, so the right tail is about 0.025 and the two-tailed p-value is about 0.05.
Use the left tail for the chance of a value at or below x, the right tail for the chance of a value at or above x, and the two-tailed value when a result on either side counts, as in a standard two-sided test.
The z score itself is just a standardized distance, so it can be computed for any data. The percentile and tail probabilities assume the data are approximately normal, which is the case the normal tables describe.
The calculator evaluates the normal CDF with the regularized incomplete gamma function. In our test suite it matches published reference values such as Φ(1.96) = 0.9750021 to about nine decimal places.
We use cookies for analytics and personalized ads to help keep these tools free. Until you accept, ads stay non-personalized and analytics cookies are off. See our Privacy Policy.