Or icy road.

+1.
But theoretically possible.

In the code the motion is 12.0, not 20.0. Where did you get the 20.0 value from?

And here is the link to the histogram for a normal distribution with mean 12.0 and standard deviation 5.: http://www.4shared.com/photo/TJx8pw_r/hw3-6_histogram.html?refurl=d1url

EDIT: I see, I checked again the video and Sebastian is showing the test part with 8 iterations and distance of 20. However, in my sample of code when clicking on the NEXT button, I am having 6 iterations and distance of 12. So, seems the video and the code aren't the same. Also, the steering angle shown in the video is 2pi/10, while in the code it is 2pi/20.

Test case one says:

motions = [[2. * pi / 10, 20.] for row in range(8)]

Test case two says:

motions = [[2. * pi / 20, 12.] for row in range(number_of_iterations)]

so distances 12 and 20, and steering angles for 2 pi / 20 and 2 pi or 10 are used. Your histogram shows, you can go negative with a base distance of 12, but it should not happen very often. I am also not sure your histogram was generated correctly. I did a search on wolframalpah.com with "gaussian distribution mean 12 variance 5". That shows standard deviation as sqrt(5). The notes at the top of the sample code say the noise values are variance, not standard deviation. So your chart should use a standard deviation or sqrt(5), not 5. The graph on the wolframalpha page shows dropping to basically zero at about 5.5 and 18.5. Here is a link to that page:

gaussian distribution mean 12 variance 5

Well, thanks I now know where is the confusion. In the notes you have the following comment:

 # A good way to include noise in the sense step is to
 # add Gaussian noise, centered at zero with variance
 # of self.bearing_noise to each bearing. You can do this
 # with the command random.gauss(0, self.bearing_noise)

So, this clearly let you think random.gauss(0, self.bearing_noise) is taking variance as the second argument while the official documentation on http://docs.python.org/library/random.html says random.gauss(mu, sigma) is taking standard deviation as the second argument.

If you look at the code for measurement_prob(), you will see Sebastian is updating the error with the following formula:

 error *= (exp(- (error_bearing ** 2) / (self.bearing_noise ** 2) / 2.0) / sqrt(2.0 * pi * (self.bearing_noise ** 2)))

So, here the self.bearing_noise is in fact the standard deviation. Now, what about steering_noise and distance_noise?

Conclusion, the comment itself is wrong. A good way to include noise centered at zero is not to use random.gauss(0, self.bearing_noise) it is to use random.gauss(0, sqrt(self.bearing_noise)).

Can Andy clarify if the provided values are standard deviation or variance?

Answered here http://www.udacity-forums.com/cs373/questions/16527/variance-vs-standard-deviation-ambiguity-in-hw-3-6

Noise is standard deviation, not variance. The comment is wrong.

Actually, the robot world in this assignment is documented to not be cyclic, and move() does not wrap around as the earlier assignments did.

Read the comment for world size in the homework. This world is NOT cyclic. The initialization makes sure the random starting position is within those world boundaries, but movement is allowed outside of that.