The effect of multiple samples on SD

Hi all,

This is the question I am looking at...

*Imagine you are building a wall from precast concrete blocks. Standard 20 cm Blocks are 19.5 cm high to allow for a 0.5 cm layer of mortar. In practice, the height of a block plus mortar row varies according to a Normal Distribution with mean 20.0 cm and standard deviation 0.25 cm. Heights of successive rows are independent. Your wall has 10 rows. *

(i) What is the distribution of the height of the wall?

(ii) What is the probability that the height of the wall differs from the design height of 200 cm by more than 1 cm?)

My working is as follows.

The normal distribution should be $\displaystyle (\mu, \sigma)$. $\displaystyle \mu = 20$ still because even after 10 samples the total mean should still be the same. The SD I'm having trouble with. Is it true that the SD of the sample is $\displaystyle \frac{\sigma}{\sqrt{n}}$? If it is, then I guess the SD should be 0.079, giving an answer of

$\displaystyle N(\mu = 20, \sigma = 0.079)$ for (i)

For (ii) I believe (if (i)) is correct, that it should be a case of normalizing X then looking up the Z tables, resulting in a Z score of 201 - 200 / 0.079 = 12.658.

Obviously something that has 12.658 SD away from the mean in normal distribution is next to impossible, which makes me suspect I've done something wrong in the working.

Can anyone please check my working? Thank you.