Peak in probability distribution moves in normpdf when changing lower bound for input vector

I am trying to compare some data with a computed normal approximation to the dataset. I computed the sample mean and standard deviation the normal ways (mean and std)', I've come up with 40K and 6K (to 1 SF). When I try to plot this distribution using a simple statement:

plot(normpdf(10e3:70e3,40e3,6e3))

It shows the peak in the probability distribution as 30K! When I use a different lower bound for the vector to plot, it moves the probability peak further (e.g., if I start at 20K, the peak moves to 20K).

It appears that the peak in the distribution is appearing at $MEAN- /$LOWER_BOUND, as when I set the lower bound to zero, I get the expected behavior of a normal PDF centered at 40K. The standard deviation of 6K appears to be correctly used in all cases.

Similar behavior is manifested when using a negative lower bound: using the below command changes the peak in the probability displayed to 60K

plot(normpdf(-20e3:70e3,40e3,6e3))

Answer 1

[David Goodmanson]

Hi Chris, try

x = 10e3:70e3;
plot(x,normpdf(x,40e3,6e3))

The problem occurs because if you create y = f(x) and use plot(y), the plot command has no way of knowing what the x array might have been. Without an explicit x input, the x axis is taken to be the y array indices 1:length(y).

[Chris Ostrom]

That makes a lot of sense, I assumed that the information somehow was transmitted between the functions. I can confirm that plotting the array and NORMPDF(array) does indeed provide the expected results.

Thanks!