How do you what number is exactly 1, 2 or 3 standard deviations away from the mean?

Question

For example, the question is The population of scores on the SAT forms a normal distribution with(mu= 500) and sigma = 100. A random sample of n= 16 students is used, what is the probability that the sample mean will be greater than M=525?

the answer in the textbook says that 525 is above the mean by 25 points so its exactly 1 SD or 1 Standard error so z = +1.00

However, how do you know what values signify 1 SD and which numbers are for the second SD and so on? I'm also assuming that when you get the 1 SD it is also just z= 1.00 because the SD is 1.

Answer 1

The standard error for the mean is sigma/square root sample size = 100/sqrt(16) = 25, so 25 is one standard deviation for the sample mean relative to the population mean.

sample mean of 525 is one standard deviation above the population mean and corresponds to z = +1. sample mean of 550 is two standard deviations above the population mean and corresponds to z = +2.

Conversely:

sample mean of 475 is one standard deviation below the population mean and corresponds to z = -1.

sample mean of 450 is two standard deviations below the population mean and corresponds to z = -2.