Long description: CumulativeDistFct

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The graph displays the cumulative distribution function, \(\Phi(z)\), for a standard normal distribution.

Alt text: The graph displays the cumulative distribution function, \(\Phi(z)\), for a standard normal distribution.

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  • The horizontal axis is labeled with values ranging from \(-2\) to at least \(3\), representing the variable \(z\).
  • The vertical axis represents the cumulative probability, \(\Phi(z)\).
  • The plotted curve is a smooth, monotonically increasing sigmoid shape, characteristic of a cumulative distribution function.
  • The function starts near \(0\) for values of \(z\) far to the left (e.g., at \(z=-2\)).
  • The curve rises steeply around \(z=0\), where \(\Phi(0) = 0.5\).
  • As \(z\) increases further to the right, the curve flattens out, approaching a limit of \(1\).
  • A dashed horizontal line is drawn at a probability value of \(1\), indicating the upper bound of the cumulative distribution.

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