Normal Distribution

Functions > Statistics > Probability Distributions > Normal Distribution

Normal Distribution

The following functions are associated with the normal equation:

Click to copy this expression

<region id="ID0EL6GAB" top="76.800000000000011" left="76.800000000000011" height="53.445333527326589" width="215.7026666369041" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="1">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <mult />
      <apply>
        <div />
        <real>1</real>
        <apply>
          <mult />
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <scale />
              <real>2</real>
              <id xml:space="preserve">π</id>
            </apply>
          </apply>
          <id xml:space="preserve">σ</id>
        </apply>
      </apply>
      <apply>
        <id xml:space="preserve">exp</id>
        <apply>
          <mult />
          <apply>
            <div />
            <real>-1</real>
            <apply>
              <scale />
              <real>2</real>
              <apply>
                <pow />
                <id xml:space="preserve">σ</id>
                <real>2</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <parens>
              <apply>
                <minus />
                <id xml:space="preserve">x</id>
                <id xml:space="preserve">μ</id>
              </apply>
            </parens>
            <real>2</real>
          </apply>
        </apply>
      </apply>
    </apply>
  </math>
</region>

• dnorm(x, μ, σ)—Returns the probability density for value x.

• pnorm(x, μ, σ)—Returns the cumulative probability distribution for value x.

• qnorm(p, μ, σ)—Returns the inverse cumulative probability distribution for probability p.

• rnorm(m, μ, σ)—Returns a vector of m random numbers having the normal distribution.

• cnorm(x)—Returns the cumulative probability distribution with mean 0 and variance 1.

Arguments

• x is a scalar or vector of real values.

• μ is a real mean.

• σ is a real standard deviation, σ> 0.

• p is a real probability, 0 ≤ p ≤ 1.

• m is an integer, m > 0.