Normal Distribution with random mean and standard deviation When trying to code this in R, I'm getting very confused about what to do. Apologies if my terminology is incorrect but I would be grateful for any advice.
The Problem:
I have been given two normal distributions for the mean and standard deviation of rat weights. So:


*

*The mean rate weight is itself a normal distribution with a mean of 1.68 and a standard deviation, or confidence interval, of 1.81 (mean = 12.68, SD = 1.81)

*The standard deviation is itself a normal distribution with a mean of 11.19 and a standard deviation of 3.2 (mean = 11.19, SD = 3.2)


Summary
Mean Rate Weight: dnorm(Mean = 12.68, SD = 1.81)
Standard Distribution of Rat Weight: dnorm(Mean = 11.19, SD = 3.2)
The Question:
In R, how to a code this to have a Monte Carlo run of 50,000 samples? Is the following example correct?
 MC_Runs = 50000

 Rat_Weight = rnorm(MC_Runs,
                   mean = rnorm(MC_Runs,mean = 12.68, sd = 1.81),
                   sd= rnorm(MC_Runs,mean = 11.19, sd = 3.2))

 A: Your solution is correct, assuming the two normal random variables are independent. According to the R documentation of rnorm, you can input a vector of means and standard deviations for the mean and sd arguments respectively. 
To verify, consider this toy example:
n <- 3 
mean_vector <- c(0,10,100)
sd_vector <- c(1,1,1)

rnorm(3, mean=mean_vector, sd=sd_vector)

Some output:
[1]  1.049676 11.566033 98.481899
[1] -1.374753  9.078215 99.465803
[1]  3.056377  9.837055 98.842553

Clearly the first variate for each simulation is $N(0,1)$ distributed, the second is $N(10,1)$ distributed, and the third is $N(100,1)$ distributed.
A: The code will work, and will give you random samples from a normal distribution with the set of means and SDs with the defined distributions. What you should note is that the generated sample of 50000 might not explore all the candidate pairs of the mean and SD values that are used to generate it. If that is of concern to you, then you might want to try Latin hyper-cube sampling. 
