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# Can anyone explain how the phi(x) works?

Can anyone explain in what alternate universe or notation the Phi(x) function in Excel 2019 (probability based on the standard normal density function) works? In my education and in the textbook I saved, Phi(0) = 50%, Phi(<0) = lower than 50% probability. Phi(0.75) = 0.7734

Looking at the excel help page,

=PHI(0.75) is” The value of the density function for a standard normal distribution. With a result on the help page of 0.301137432. This what I get when I enter it into Excel also.

Based on how it is traditionally taught Phi(0.75) should be greater than 50% (77.34%), not 30%.

I hope someone can explain what universe Excel is in and what units of X represent average, average +1 standard deviation, average - 1 standard deviation, etc.

2 Replies

# Re: Can anyone explain how the phi(x) works?

The function PHI(x), which I had never come across, appears to be the probability density function

= NORM.DIST( x, 0, 1, FALSE )

[with zero mean and unit standard deviation] which shows a peak at x=0 and tails off in both directions. It is not the cumulative value

= NORM.DIST( x, 0, 1, TRUE )

which has a value of 50% at x=0, rising to 100% as x increases and dropping to 0% as it decreases

# Re: Can anyone explain how the phi(x) works?

OK, that appears to fit the bill of what I need.  Thank you

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