Electron noise

[wtrow]

The number of free electrons in a metal fragment is measured with a measurement error that
is normally distributed. More specifically, if there are n free electrons, the number Y = n+X
is recorded where X has a normal distribution with mean 0 and standard deviation S = 0.43.
If Y is rounded to the nearest integer, what is the probability that we get the right answer?

I'm not really sure if I understand this one. I found in my book that S^2=Var[X], yet I don't see how it relates to this problem. Can anyone tell me what I should do?

 

[tkhunny]

It's rounded. You will get the wrong answer if you get more tha 0.50 away from the mean, either direction.

Calculate the z-score for 0.50.

 

[wtrow]

I see now, it was just simple statistics. Thank you!