Take a random variable (X) distributed normally with a mean 4 and variance 4 (i.e., X~N (4,4). [You will need a standard normal distribution table to complete this question].

• Say you want to make a new random variable (Z) from (X) that is distributed standard normal. How do you transform X to achieve this?

If you draw a number at random from the X distribution, what is the probability it is less than zero? Greater than zero?Lets say you draw a number randomly from the distribution of X. What is the probability that you draw a number that is more than 0.5 standard deviations away from the mean (in either direction)?

Please, show formulas and calculations!!!