Àwọn

Wá àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò àti àwọn ìṣàmúlò-ètò ìṣàmúlò-ètò fún fálù ìṣàmúlò-ètò.

Àwọn

Àwọn ìṣàmúlò-ètò

Àwọn ìṣàfarawé àwọn ìṣàmúlò-ètò

Ìgbàdúró ìsàlẹ̀-ilà (x₂) ?

Àwọn ìkúndùn. Fi àwọn àwọn ààyè-iṣẹ́ kùnà fún ìṣàmúlò-ètò fálù kan.

P(X ≤ x) —

P(X ≥ x) —

P(x ≤ X ≤ x₂) —

Àwọn ìṣàmúlò-ètò —

Àwọn Àtòjọ-ẹ̀yàn àwọn ìṣàmúlò-ètò

Ńlà àwọn àwọn ààtò àtòjọ-ẹ̀yàn yìí?

Àkóónú ìṣàmúlò-ètò yìí

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.

Àwọn Àtòjọ-ẹ̀yàn

Kini iyatọ laarin pdf ati cdf?

The probability density (pdf) is the height of the bell curve at x; it is not a probability by itself. The cumulative distribution (cdf) is the area under the curve up to x, which gives the probability of a value at or below x.

Kini idi ti àwọn ìṣàmúlò-ètò tí àwọn fálù ìṣàmúlò-ètò jẹ́ ìtàn?

Fún ìṣàfihàn tí a ǹlọ́wọ́ lọ́wọ́lọ́wọ́ bí a tí ǹró, àwọn ààyè kaǹkẹ́ ní àwọn ìṣàfihàn sáà - àwọn ìjánu-i

Kini ofin 68-95-99.7?

Fún ìṣàfarawe-ọ̀rọ̀ ìṣàfarawe-ọ̀rọ̀ ìṣàfarawe-ọ̀rọ̀, 68% tí àwọn fálù náà tí wa ni inú ìṣàfarawe-ọ̀rọ̀ kan tí a fi pamọ́, 95% ni inú meji náà, 99.7% ni inú mẹ́ta náà. O jẹ́ ọna tí o lè gbàgbọ́ pé bí àwọn fálù náà ṣe lè jẹ́ àìdájú àwọn ààyè tí a kò bá kọ́ọ̀kan.

Bawo ni mo ṣe lè rí ìgbàdálẹ̀ laarin àwọn fálù meji?

Enter the lower value as x and the upper value as x₂; the calculator returns P(x ≤ X ≤ x₂) by subtracting the cumulative probability at the lower point from the one at the upper point.

Kini ìyatọ̀ laarin ìṣàfarawé àwọn ìṣàmúlò-ètò àti àwọn ìṣàmúlò-ètò ìpéwọ̀n?

The standard normal is just the normal distribution with a mean of 0 and a standard deviation of 1. Converting any value to its z-score maps it onto the standard normal, which is how this tool computes probabilities for any μ and σ.

Ńlà tí àtòjọ-ìdáràn mì fẹ́ jẹ́ ìṣàfarawé nípa ìṣàfarawé?

Kò ní àwọn àkóónú àìdálẹ̀ tòotọ ní pàtó, àwọn àwọn àkóónú náà ní ìròyìn látigbá tí àkóónú náà jẹ́ àwọn àkóónú tí a tí ìṣàfarawé ní pàtó. Fún àwọn àkóónú àìdálẹ̀ tí a tí ìṣàfarawé nípa ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé nípa àwọn àkóónú tí a tí ìṣàfarawé.

API — ló àwọn ìṣàmúlò-ètò yìí láti inú ìṣàmúlò-ètò

Fi àwọn ìṣàmúlò-ètò yìí kọ̀ǹpútà yìí láti jẹ́ ààyè-iṣẹ́ JSON tí a tí fi pamọ́ - kò ní bọ́tìnì kan tí a fẹ́. Fi àwọn fálù ààyè-iṣẹ́ sílẹ̀ sí bí àwọn àwọn ìṣàmúlò-ètò àti JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Ka àwọn àkọlé API kíkún →

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

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);

Results are estimates for general guidance only, not financial, medical or tax advice.

Àkóónú ìṣàmúlò-ètò yìí

Àwọn Àtòjọ-ẹ̀yàn

Àwọn Ìṣàmúlò-ètò Ìṣàmúlò-ètò

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

curl

JavaScript fetch()

JavaScript `fetch()`