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Find the probability density and cumulative probability for a normal value.
Results update as you type.
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the standard-normal distribution, the probability density at x is 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. The probability density at x is 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. The probability density at x is the cumulative probability P(X ≤ x) (the area under the curve to the left). The standard-normal distribution is the standard 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. The calculator is a free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-to-Work example: Free-
Tambayoyi da ake yi da yawa
Mene ne bambanci tsakanin pdf da 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.
Me ya sa yiwuwar kimar daidai ba ta da komai?
For a continuous distribution like the normal, any single exact point has zero probability - only ranges have non-zero probability. That's why we report the density at x and the cumulative area rather than P(X = x).
Shin, kun san abin da kuke faɗa?
For a normal distribution about 68% of values lie within one standard deviation of the mean, 95% within two and 99.7% within three. It is a quick way to judge how unusual a value is without computing the exact area.
Ta yaya zan samu yiwuwar tsakanin kimar biyu?
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.
Mẽne ne bambanci tsakanin rabon al'ada da rabon al'ada na siffar?
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.
Shin, bayanana dole ne su zama na al'ada?
No real data is exactly normal, but the results are reliable when the data is roughly bell-shaped and symmetric. For strongly skewed or heavy-tailed data the probabilities are only approximate.
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[Translation temporarily unavailable. Please try again.] Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. [Translation temporarily unavailable. Please try again.] →
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);Results are estimates for general guidance only, not financial, medical or tax advice.