Answer:

The mean is given by:

And the standard deviation would be:

And the distribution for X+Y would be:

And the best answer would be:
D.) Mean, 6.7; standard deviation, 2.08
Step-by-step explanation:
Let X the random variable who represent the AP Art History exam we know that the distribution for X is given by:

Let Y the random variable who represent the AP English exam we know that the distribution for X is given by:

We want to find the distribution for X+Y. Assuming independence between the two distributions we have:

The mean is given by:

And the standard deviation would be:

And the distribution for X+Y would be:

And the best answer would be:
D.) Mean, 6.7; standard deviation, 2.08