NORMDIST

What it does

NORMDIST(x, mean, standard_dev, cumulative)

NORMDIST(x,mean,standard_dev,cumulative) is the compatibility normal distribution. TRUE returns the probability up to x; FALSE returns a density. Standard deviation must be positive.

Try it

=NORMDIST(10,10,2,TRUE) returns 0.5. At the mean, half the distribution lies below the input. With FALSE the density is about 0.1994711402.

Quirks

Nonnumeric numeric arguments give #VALUE!. A nonpositive standard deviation gives #NUM!. A density is not a point probability and can exceed one when the scale is small. The compatibility name does not imply that its numerical stages are identical in every Excel build.

How to implement

For a general CDF first standardize using binary64 u=(x-mean)/sigma, then apply the standard wrapper. For the standard-normal CDF, the current measured wrapper stores z=R(abs(x)*c), with binary64 c given by bits 0x3fe6a09e667f3bcd. Evaluate the public ERFC body at z, halve it, and select that half for a negative argument or 1-half for a nonnegative argument. Flush the final subnormal under the current publication rule. The ERFC upper factor remains open; identifying this wrapper does not solve that inner approximation.

For density, the current kernel instead stores u=R(R(x-mean)/sigma), sq=R(u*u), then evaluates E=EXP(-sq/2), divides E by sigma at a stored site and finally multiplies by binary64 0x3fd9884533d43651. Calling a previously flushed PHI and dividing later changes the route. R means 64-bit-significand rounding followed by a binary64 store.

Rust code

2 normdist "NORMDIST" (4, 4) [V "x", V "mean", V "standard_dev", V "cumulative"] |s, a, sv| {
    let [x, m, sd_] = nums::<3>(s, a)?;
    out(s, nl::norm_dist_kernel(x, m, sd_, flag(s, a, 3)?))
}

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

NORM.DIST is the modern spelling. NORM.INV and NORM.S.INV map probabilities back to values.

Named variants

No named variants are recorded yet.