As a class we created a table listing the distribution in the first column, the mean in the second and the standard deviation in the third column. We filled it in with all the rules for transforming distributions including adding and subtracting distributions.  Students studied this for the test.

Students should first find the new mean and standard deviation by adding the means and adding the variances. After this, they need to draw and label a Normal curve! Once a Normal curve is drawn and labeled, the students had no problem finding the probability. They have been doing that for months.