# What is the distribution of the height of the wall and the probability that the height differs of height 200cm?

by more than 1cm

A wall is made from precast blocks. Standard 20cm blocks are 19.5cm high to allow for a 0.5cm 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 0.25cm. Heights of successive rows are independent. The wall has 10 rows.

Some help with this question would be really good especially in relation to what the question is asking. Thanks

Relevance

What is the distribution? It is the sum of independent normal distribution (each row's height it normally distributed), so the total wall's height follows a normal distribution.

The second part of the question asks what is the probability of the height being within 1 cm of 200cm.

For independent variables, sum the means and sum the variances. For one row, the variance = standard deviation squared = 1/16. So for 10 rows, the variance is 10/16. So the standard deviation is sqrt(10/16) = sqrt(2.5) cm = 1.58 cm.

You want an error of less than 1cm. 1 cm = 1 / 1.58 = 0.63 standard deviations. So look up a z-table from there. Since about 2/3 of the population is with +/- 1 standard deviation, I expect about 0.5 to be within +/- 0.63 standard deviations

(Continued). So look up 0.63 on a z-table. Assume the number is 0.7 (it's not, I'm just guessing). That means that 0.7 of the population is below (mean + 0.63 SDs), and also that 0.7 of the population is above (mean - 0.63 SDs). And that means 1-0.7=0.3 of the population os below (mean - 0.63 SDs), and so 0.7 - 0.3 = 0.4 probability of the height being mean +/- 0.63 SDs, i.e. 200 cm +/- 1 cm.

Adjust that answer depending what the actual value is in the z table (normal distribution table).