What you need is:

data = rnorm(n=100, mean=100, sd=15) #generate data as an example. Use your own here.

data.z = (data - mean(data, na.rm=T)) / sd(data, na.rm=T)

Please be aware that this does not "transform a vector of data into normal distribution". What z-transformation does is map data that is already normally distributed to the standard normal distribution (i.e., mean=0, sd=1). The normal distribution of the vector, however, is an assumption and not the consequence of the operation.

Thanks, Reutter. My raw datat is normallly distributed. I will adopt you method.

Lu Sun

The function scale() has being designed for task like that:

scale(X, center = TRUE, scale = TRUE)

@Raúl nice, I didn't know that function. This greatly enhances readability.

Only one caveat: the scale function always returns a matrix even if you enter a vector. If you want the vector, you need to as.vector(scale(X, center=T, scale=T)).