Final answer:
The standard deviation of x is given as 4, which remains unchanged regardless of the value of x unless the data itself changes. Standard deviation is a measure of how spread out numbers are and is calculated as the square root of the variance.
Step-by-step explanation:
If the standard deviation of a variable is given as 4, and the z-score for y = 4 is z = 2, it implies that y is two standard deviations away from its mean. Similarly, if x = 17 and y = 4 are both described as two standard deviations to the right of their means, the standard deviation of x would remain the same as the given standard deviation for y, which is 4. In statistics, the standard deviation remains constant for a data set unless the data itself undergoes a transformation.
As for the z-score of -4 (Solution 6.2), indicating that x = -3 is four standard deviations to the left of the mean, this also supports the idea that the standard deviation for x is consistent, as it is a measure of dispersion that does not depend on the data value but rather on the spread of all values around the mean.
To calculate standard deviation, the formula involves taking the square root of the variance, often symbolized as o for population or s for a sample. Therefore, given a variance of 62, the standard deviation would be o = √36 = 6.