Kalkaaliyihii Qaybsiga caadiga ahaa
Hesho tirada ugu badan ee suurtogalnimada iyo suurtogalnimada cumulative ee qiimaha caadiga ah.
Natiijooyinka cusbooneysiinta sida aad ku qorto.
Ku saabsan Kalkaaliyahan
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.
Su'aalaha badanaa la isweydiiyo
Waa maxay farqiga u dhexeeya pdf iyo cdf?
The isku dheelitirka suurtogalnimada (PDF) waa dhererka curve bell at x; ma aha in ay suurtogal tahay oo keliya. The qaybinta cumulative (CDF) waa dhulka hoos ku curve ilaa x, taas oo siineysa suurtogalnimada qiimaha at ama hoos u x.
Maxaa keenay in ay suurtogalnimada qiimaha saxda ah zero?
Si loo qaybiyo sii socda sida caadiga ah, mid kasta oo ka mid ah dhibcood oo kaliya sax ah waxaa jira suurtagalnimada zero — oo kaliya waa in ay leeyihiin kala duwanaansho aan-zero suurtagalnimada. Waa sababta aan u sheegno tirada x iyo dhul ku soo ururay ka badan P (X = x).
Waa maxay xeerka 68-95-99.7?
Si loo qaybiyo caadiga ah oo ku saabsan 68% qiimaha ku dhex jira mid ka mid ah kala duwanaanshaha caadiga ah ee dhexdhexaad ah, 95% laba iyo 99.7% saddex ka mid ah. Waa hab deg deg ah oo lagu garto sida aan caadi ahayn qiimaha waa aan xisaabinta dhulka saxda ah.
Sidee baan u helaa in ay suurtogal tahay u dhexeeya laba qiimo?
Ku dar qiimaha hoose sida x iyo qiimaha sare sida x₂; xisaabinta ku soo laabtay P (x ≤ X ≤ x₂) by ka bixitaanka in la isku darka ah ee suurtogalnimada ah ee meesha hoose ka mid ah mid ka mid ah meesha sare.
Waa maxay farqiga u dhexeeya qaybinta caadiga ah iyo caadiga ah ee caadiga ah?
The caadiga ah standard waa kaliya qaybinta caadiga ah oo leh dhexdhexaad ah 0 iyo ka noqnoqda caadiga ah ee 1. U beddelidda wax kasta oo qiimo ah si ay z-score maps uu ku standard caadiga ah, taas oo ah sida qalabkan u xisaabiyo suurtogalnimada in mid kasta oo μ iyo σ.
Ma data aan u baahan yahay in ay si buuxda caadi ah?
No xogta dhabta ah waa si dhab ah caadi ah, laakiin natiijada waa la aamini karaa marka xogta waa sicir-dhiig-shaped iyo sifooyinka. Si aad u xoog badan oo qalafsan ama culus-tailed xogta in la filayo waa kaliya in la qiyaaso.
API — isticmaal xisaabinta ka code
Wici xisaabinta sida free JSON endpoint - key ma loo baahan yahay. Dib u soo dir qiimaha goobta hoos ku qoran sida parameters su'aal ama JSON. Wax kasta oo aad ka maqan tahay isticmaalaa default la mid ah ee boggani waa hore loo buuxiyey la; parameter aan la aqoon waa 400, marnaba ma aha zero maqan. Akhri dhammaan API xuquuqda →
Xarafka
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);Natiijooyinka waa tirakoobka loogu talagalay tilmaamaha guud oo keliya, maaha dhaqaale, caafimaad ama talo bixin canshuur.