I-Calculator yokusabalalisa okujwayelekile
Thola ubukhulu besimo sesimo kanye nesimo esiphelele sesimo se
Iziphetho zivuselelwa uma ubhala.
Malunga nale khadi
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.
Imibuzo ebuzwa kaningi
Yini ushintsho phakathi kwe-pdf ne-cdf?
Ubukhulu besimo sesimo (pdf) yiphakamo ye-bell curve ku-x; akuyona isimo sesimo sesimo. Ukusabalalisa okuqotho (cdf) yindawo ngaphansi kwe-curve kuze kube yi-x, okunikeza isimo sesimo sexabiso ku-x noma ngaphansi kwayo.
Kungani ingozi yenani elifanele liyi zero?
Ukusabalalisa okuqhubekayo njengento ejwayelekile, noma yisiphi isiphetho esicacile sinomqondo ophansi - amabanga kuphela anengqondo engekho emthethweni. Lokhu kusho ukuthi sicela ubukhulu ku-x kanye nendawo eqoqiwe endaweni ye-P (X = x).
Yini imithetho ye-68-95-99.7?
Ukusabalalisa okujwayelekile, cishe i-68% yamaxabiso akhona ngaphakathi kwe-standard deviation eyodwa ye-mean, i-95% ngaphakathi kwe-2 ne-99.7% ngaphakathi kwe-3. Kuyindlela ekhawulelayo yokucabanga ukuthi ixabiso linjani ngaphandle kokubala indawo efanele.
Ngiyithola kanjani ingozi phakathi kwamaxabiso amabini?
Ngeza inani eliphansi njenge x nenani eliphezulu njenge x₂; i-calculator ibuyisela i-P(x ≤ X ≤ x₂) ngokususa i-cumulative probability engxenyeni ephansi kusuka kuleyo engxenyeni ephezulu.
Yini ushintsho phakathi kokuhlukaniswa okujwayelekile nesimo esijwayelekile?
Isilinganiso esijwayelekile siyisilinganiso sokusabalalisa esijwayelekile esiphakathi kuka-0 nesilinganiso sokungalingani ko-1. Ukushintsha noma yisiphi isilinganiso sibe yiz-z-score isiza isilinganiso esijwayelekile, okuwukuthi indlela le thuluzi elibala ngayo i-probability nganoma iyiphi i-μ ne-σ.
Ingabe idatha yami kufanele ibe ngempela ejwayelekile?
Akukho data ekhona ejwayelekile, kodwa izimpendulo zithembekile uma idatha ifana ne-bell futhi ilingana. Ku-data eqinile noma enzima-i-tailed, i-probability ilinganiselwe kuphela.
API — sebenzisa le calculator kusuka kukhodi
Nquma le calculator njenge JSON evulekile yendawo yokuqeda - akukho isithonjana esidingekayo. Thumela amaxabiso endawo ngezansi njengezilungiselelo zombuzo noma i-JSON. Noma yini ongayishiya isebenzisa iphutha elifanayo elifakwe ngaphambili lekhasi; ipharamitha engaziwa yi-400, ayikho i-zero emnyama. Funda i-API egcwele →
Ingxenye yendawo
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);Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.