Laser length tool has an average error of 0cm, and the standard deviation error of 1 cm.

We are measuring the length of a table. And we repeat that 20 times. What is the probability that the error is less than 0.5 cm?

I understand it like this;

The laser tool is distributed normal:

$\displaystyle X = N(0,1)$

We take the 20 mesaurments of the table, and that is also distributed normal like this:

$\displaystyle Y = N(0,\frac{1}{\sqrt{20}})$

So with this Y value, I calculate with $\displaystyle \phi$ function and look at the standard normal distribution table, and get..

$\displaystyle \phi(\frac{0.5-0}{0.2236}) = 0.98$

Is this correct?, Or I have missed something?