Problems with NORMDIST
 

Should I be concerned that NORMDIST(4.92, 4.94, 0.08, FALSE) returns
4.83? This should be the noncumulative (density, mass) function
associated with the normal distribution. Surely it cannot exceed 1
because the entire area under the curve cannot exceed 1, by definition
of probability distribution. The related NORMSDIST problem:
NORMSDIST(-0.25, 0, 1, FALSE) returns 0.3866, which seems reasonable.

Can someone please reconcile the answers, or explain why Excel allows
probability distributions to have values greater than one?

Thank you.

Problems with NORMDIST
 

4.92 is 25 standard deviations to the left of the mean. Until xl2003, the
Normal distribution function was known to give bad results deep into the
tails. Anything greater than -3 standard deviations is very small. For 25
standard deviations, you probably would be safe in assuming a probability of
0. Also, note that the probability of any single value in a continuous
distribution is considered to be zero.

http://support.microsoft.com/kb/827371/en-us
Description of the NORMDIST function in Excel 2003

--
Regards,
Tom Ogilvy

"Kevin" wrote in message
oups.com...
Should I be concerned that NORMDIST(4.92, 4.94, 0.08, FALSE) returns
4.83? This should be the noncumulative (density, mass) function
associated with the normal distribution. Surely it cannot exceed 1
because the entire area under the curve cannot exceed 1, by definition
of probability distribution. The related NORMSDIST problem:
NORMSDIST(-0.25, 0, 1, FALSE) returns 0.3866, which seems reasonable.

Can someone please reconcile the answers, or explain why Excel allows
probability distributions to have values greater than one?

Thank you.

Problems with NORMDIST
 

This time it is not a problem with Excel :-) Kevin uses a mean of 4.94
and a standard deviation of 0.08, so 4.92 is about two standard
deviations from the mean.

You need to change the fourth parameter from FALSE to TRUE, then you
get

NORMDIST(4.92; 4.94; 0.08; TRUE)

= 0.401293674

which is the correct result. With FALSE, you get the value of the
density function, which can be well bigger than 1. With TRUE, you get
the desired probability (=(cumulative density) value.

HTH
Matthias Kläy
--
www.kcc.ch

"Tom Ogilvy" wrote:

4.92 is 25 standard deviations to the left of the mean. Until xl2003, the
Normal distribution function was known to give bad results deep into the
tails. Anything greater than -3 standard deviations is very small. For 25
standard deviations, you probably would be safe in assuming a probability of
0. Also, note that the probability of any single value in a continuous
distribution is considered to be zero.

http://support.microsoft.com/kb/827371/en-us
Description of the NORMDIST function in Excel 2003


"Kevin" wrote
Should I be concerned that NORMDIST(4.92, 4.94, 0.08, FALSE) returns
4.83? This should be the noncumulative (density, mass) function
associated with the normal distribution. Surely it cannot exceed 1
because the entire area under the curve cannot exceed 1, by definition
of probability distribution. The related NORMSDIST problem:
NORMSDIST(-0.25, 0, 1, FALSE) returns 0.3866, which seems reasonable.

Can someone please reconcile the answers, or explain why Excel allows
probability distributions to have values greater than one?

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Problems with NORMDIST
 

Your assumption that the density cannot exceed 1 is incorrect. To see this
easily, note that almost all of the cumulative area is contained within
mean+/-3*SD, which in your case is a region that is only 0.48 wide; therefore
for that area to approach 1, the height must exceed 1 in at least part of
that region.

Alternately, you can calculate it directly for yourself from the definition
of the normal pdf
=exp(-(((4.92-4.94)/0.08)^2)/2)/sqrt(2*pi())/0.08
Note that the extra parentheses immediately following the minus sign in the
exp() function are required, because Excel follows a non-standard convention
where unary negation is higher in priority than exponentiation.

Jerry

"Kevin" wrote:

Should I be concerned that NORMDIST(4.92, 4.94, 0.08, FALSE) returns
4.83? This should be the noncumulative (density, mass) function
associated with the normal distribution. Surely it cannot exceed 1
because the entire area under the curve cannot exceed 1, by definition
of probability distribution. The related NORMSDIST problem:
NORMSDIST(-0.25, 0, 1, FALSE) returns 0.3866, which seems reasonable.

Can someone please reconcile the answers, or explain why Excel allows
probability distributions to have values greater than one?

Thank you.

Problems with NORMDIST
 

Sorry, I have to correct myself: The value of 4.92 is only 1/4th of a
standard deviation of 0.08 from the mean of 4.94, because

(4.92 - 4.94)/0.08 = -0.02/0.08 = 0.25

Then the result of 0.4 for the probability value is very plausible.

Greetings
Matthias Kläy
--
www.kcc.ch

Matthias Klaey wrote:

This time it is not a problem with Excel :-) Kevin uses a mean of 4.94
and a standard deviation of 0.08, so 4.92 is about two standard
deviations from the mean.


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Problems with NORMDIST
 

Bad math on my part, read something other than what you actually posted (red
faced) - sorry about that.

--
Regards,
Tom Ogilvy

"Tom Ogilvy" wrote in message
...
4.92 is 25 standard deviations to the left of the mean. Until xl2003, the
Normal distribution function was known to give bad results deep into the
tails. Anything greater than -3 standard deviations is very small. For
25
standard deviations, you probably would be safe in assuming a probability
of
0. Also, note that the probability of any single value in a continuous
distribution is considered to be zero.

http://support.microsoft.com/kb/827371/en-us
Description of the NORMDIST function in Excel 2003

--
Regards,
Tom Ogilvy

"Kevin" wrote in message
oups.com...
Should I be concerned that NORMDIST(4.92, 4.94, 0.08, FALSE) returns
4.83? This should be the noncumulative (density, mass) function
associated with the normal distribution. Surely it cannot exceed 1
because the entire area under the curve cannot exceed 1, by definition
of probability distribution. The related NORMSDIST problem:
NORMSDIST(-0.25, 0, 1, FALSE) returns 0.3866, which seems reasonable.

Can someone please reconcile the answers, or explain why Excel allows
probability distributions to have values greater than one?

Thank you.

Problems with NORMDIST
 

Jerry,

You are right, and that answers my question. I guess the density has
to exceed 1 in order for the area under the curve to sum to 1. Thanks
so much!

Kevin


Jerry W. Lewis wrote:
Your assumption that the density cannot exceed 1 is incorrect. To see this
easily, note that almost all of the cumulative area is contained within
mean+/-3*SD, which in your case is a region that is only 0.48 wide; therefore
for that area to approach 1, the height must exceed 1 in at least part of
that region.

Alternately, you can calculate it directly for yourself from the definition
of the normal pdf
=exp(-(((4.92-4.94)/0.08)^2)/2)/sqrt(2*pi())/0.08
Note that the extra parentheses immediately following the minus sign in the
exp() function are required, because Excel follows a non-standard convention
where unary negation is higher in priority than exponentiation.

Jerry

"Kevin" wrote:

Should I be concerned that NORMDIST(4.92, 4.94, 0.08, FALSE) returns
4.83? This should be the noncumulative (density, mass) function
associated with the normal distribution. Surely it cannot exceed 1
because the entire area under the curve cannot exceed 1, by definition
of probability distribution. The related NORMSDIST problem:
NORMSDIST(-0.25, 0, 1, FALSE) returns 0.3866, which seems reasonable.

Can someone please reconcile the answers, or explain why Excel allows
probability distributions to have values greater than one?

Thank you.