1. A professor calculates total course grade scores by summing the midterm and final exam scores. He know that the midterm exam scores have mean 89.1 and standard deviation 15.0 and the final exam scores have mean 94.4 and variance 13.6. The midterm and final exam scores have a correlation of 0.85. What will be the MEAN and the VARIENCE of the total course grade scores? Please give both quantities, and show all the steps.
2. A variable X is distributed as a normal with mean 78 and variance 125. What is the probability that a randomly chosen observation has a value greater than 100?
3. A random variable is randomly distributed, with mean 25 and standard deviation 9.5. What is the probability that a randomly selected observation has a value between 20 and 35?
4. A telemarketing company calculates that the probability of any dialed number being answered by a live person is 14%. If the company makes 15 calls, what is the probability that exactly two calls are unanswered?