Help Describing Graphical Solution

Good day. Since this is my first time here, (moderators) let me know if I should have posted this inquiry somewhere else, please.

Many years ago, I was shown a graphical method for presenting a probability distribution, on "probability" paper. (X-axis = the variable of interest, Y-axis = values of the probability function from 0.01 to 99.99. The paper itself resembles semilogarithmic graph paper, the X-axis being linear.)

The method assumed that the data under analysis were normally distributed. Then, by plotting the average and points at + and - 1 standard deviation away, one can construct a three-point line that represents the probability distribution of the data being analyzed.

My question -- It seems that it should be possible to determine the equation of the line, in the case above. I have tried a couple of different functional forms of equations, however (such as Y = a*e**(b*X) ), and had no success. (Y = probability, X = variable being studied.)

Can anyone suggest the form of equation I should use (example also, please) that would allow me to determine the mathematical expression that describes the line ?

Second part of the question -- what would the form of the equation be that would describe such a line drawn on LOG probability paper (logarithmic X-axis) ?

Thanks for considering this question.

Mel L.