Normal Distribution Calculator

Ita shuwa kuti uine chokwadi chekuti mhedzisiro yemubvunzo unoratidzika kunge iri nani pane iyo yaunofungidzira.

P(X ≤ x) —

P(X ≥ x) —

P(x ≤ X ≤ x₂) —

Z-score —

Kuita —

Zvinyorwa zvinogadziridzwa paunenge uchinyora.

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Nezve iyi kalkulator

The normal (Gaussian) distribution is the classic symmetric bell curve that describes heights, measurement errors, test scores and countless other natural quantities. Given a value x, a mean μ and a standard deviation σ, this calculator returns the probability density at x, the cumulative probability P(X ≤ x) (the area under the curve to the left), the right-tail probability P(X ≥ x) and the equivalent z-score, and plots the curve.

Internally it converts x to a z-score, z = (x − μ) / σ, then evaluates the standard-normal cumulative distribution with an accurate error-function approximation. Enter an optional upper bound x₂ to get the range probability P(x ≤ X ≤ x₂), computed as the difference of the two cumulative values.

Worked example: for a distribution with μ = 100 and σ = 15, a value of x = 120 has a z-score of (120 − 100) ÷ 15 ≈ 1.33, so P(X ≤ 120) is about 90.9% and the right tail P(X ≥ 120) about 9.1%. This is the tool behind IQ scores, control charts and the empirical 68–95–99.7 rule.

Zvimwe zvinobvunzwa zvakanyanya

Chii chinonzi chiyero pakati pePDF neCDF?

Kusiyana kwezviyero zvemasimba emagetsi kunoonekwa sezviyero zvemasimba emagetsi. Kusiyana kwezviyero zvemasimba emagetsi kunoonekwa sezviyero zvemasimba emagetsi. Kusiyana kwezviyero zvemasimba emagetsi kunoonekwa sezviyero zvemasimba emagetsi.

Nei kumbobvira kuitika kwechiito chekufungidzira chisina kumbobvira chaitika?

Kuti uwane kugoverwa kwakaomarara sekwakajairika, chero imwe chete nzvimbo imwechete ine mukana wekuti iite chinhu chisina kuitika. Izvozvo zvinoita kuti titore muenzaniso wekuti hunhu hwex uye nzvimbo yacho iite chinhu chisina kuitika.

Chii chinonzi 68-95-99.7 rule?

Kuti uwane kugoverwa kwakajairika, 68% yezviyero zvinongova mukati meimwe standard deviation yepakati, 95% mukati mezviviri uye 99.7% mukati mezvitatu. Ichi ndicho chikonzero chakanaka chekuziva kuti chiyero chinogona kunge chiri chakaipa pasina kumbobvira waongorora nzvimbo yacho.

Ndinogona sei kuwana mukana pakati pezviviri zviwanikwa?

Ingopinda pasi pemari se x uye pamusoro pemari se x₂; calculator inodzokera P (x ≤ X ≤ x₂) nekubvisa kuunganidzwa kwechokwadi papasi penzvimbo kubva kune imwe papamusoro penzvimbo.

Chii chinonzi chiyero chekuparadzanisa kwezviyero zvemavara?

Standard normal ndiyo chete normal distribution ine mean ye0 nestandard deviation ye1. Kushandura chero mhedzisiro kune z-score kwayo inoisa iyo pane standard normal, iyo ndiyo nzira iyo iyi chirongwa chinoongorora kufungidzira kweanenge ese μ ne σ.

Ndeapi madata angu anofanirwa kuve akanyatsojeka?

Hapana data rakanaka rinogona kuitwa kuti riite kuti zvive nyore, asi zvinoitika kana data riine umbozha uye rakaenzana. Kana data riine umbozha kana riine makumbo marefu, zvinoitika kuti zvive nyore.

API — kushandisa iyi kalkulator kubva code

Nhare iyi calculator semahara JSON endpoint - hapana chikuru zvinodiwa. Kutumira nzvimbo mavara pasi separameter query kana JSON. Chii zvachose chaunoisa kunze chinoshandisa default iyo peji iri rakasviba nayo; parameter isiri yechokwadi inonzi 400, uye haisi zero. Tora yakazara API docs →

Endpoint

GET https://calculator.free/api/v1/normal-distribution/

curl

curl "https://calculator.free/api/v1/normal-distribution/?x=120&mean=100&sd=15"

JavaScript `fetch()`

const r = await fetch(
  "https://calculator.free/api/v1/normal-distribution/?" + new URLSearchParams({
    "x": "120",
    "mean": "100",
    "sd": "15"
  }));
const data = await r.json();
console.log(data.results);

Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.

Nezve iyi kalkulator

Zvimwe zvinobvunzwa zvakanyanya

Maitiro ekuita Calculators

Endpoint

curl

JavaScript fetch()

JavaScript `fetch()`