Find probabilities

After specifying the parameter(s), the graph of the probability density function (in the case of a continuous distribution) or the graph of the probability mass function (in the case of a discrete distribution) is shown under the 'pdf' or 'pmf' tab respectively. It is possible to move the division line between the red (left hand) and blue (right hand) part of the graph, by means of a finger (Android version) or by the slider below the graph (Linux and Windows version). Thereafter the \(x\)-axis is divided in two or three parts with red, white (or grey) and blue colours. The figure at the left below shows such a partition with probabilities \(P(X < -1.645) = 0.0500\), \(P(-1.645 < X < 0.000) = 0.4500\) and \(P(X > 0.000) = 0.5000\). In the figure at the right: \(P(X < 6) = 0.4164\), \(P(X = 6) = 0.1916\) and \(P(X > 6) = 0.3920\).

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Standard normal distribution
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Binomial distribution

More accurate than moving the slider is entering the \(x\)-value in one of the two edit fields below the \(x\)-axis and pressing 'Enter'.

The graph of the cumulative probability function is shown under the 'cdf' tab. You will find the \(x\)-value below the horizontal axis and the corresponding (cumulative) probability \(P(X ≤ x)\) to the left of the vertical axis. In the figure below left: \(P(X ≤ -1.645) = 0.050\) and in the figure at the right: \(P(X <= 6) = 0.6080\).

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Cdf of a normal distribution
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Cdf of a binomial distribution