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The process for producing an image with a normal distribution and intensities ranging from 0 to 255 involves the following steps:

1. Generate a random matrix of the desired size using a normal distribution function. For example, in MATLAB, the function randn() can be used to generate a random matrix with a normal distribution.

2. Scale the values in the matrix to fit the range of 0 to 255. This can be done by multiplying the matrix by a constant factor and adding a constant offset. For example, in MATLAB, you can use the function imadjust() to adjust the intensity values of the image.

3. Convert the matrix to an image format, such as JPEG or PNG. This can be done using an image processing library or software.

4. Save the image to a file with the desired format and filename.

5. Optionally, apply image processing techniques such as filtering, smoothing or sharpening to enhance the image.