Let's say I want to generate some random data that follows the normal distribution, with a mean of 5. Will setting the standard deviation to 3 or 5 affect the distribution, that is, will it still follow the normal distribution?
I am confused on this question because the data's mean and variance are based on the data, and there are specific way of calculating them for different distribution.
*edit for clarification: I want to generate TWO data sets: both of them follow the normal distribution with a mean of 5. The 1st data set has $\mu =5$ AND $\sigma= 5 $. If I generate the 2nd data set by changing the $\sigma$ from 5 $\rightarrow$3, will the data still follow the normal distribution.