Let X be a random variable having a normal distribution with mean 100 and standard deviation 5. Let Y be a random variable, independent of X, having a normal distribution with mean 85 and standard deviation 6. Then, let the random variable W be defined as: W=2X-Y. What is the distribution of the random variable W?
Normally distributed with mean 115 and standard deviation 12.6
Normally distributed with mean 115 and standard deviation 4.0
Not a normal distribution.
Normally distributed with mean 115 and standard deviation 16.0
Normally distributed with mean 115 and standard deviation 11.7
Normally distributed with mean 185 and standard deviation 10.6
Normally distributed with mean 15 and standard deviation 11.0