The mean grade in the Fall $2020$ statistics class last semester was $78\mathrm{.}3,$ and the variance was $49.$ The distribution of grades was unimodal and symmetrical. Determine how many students are likely to fail the class $(<60),$ and how many students are likely to get an A$+(>97),$ if $60$ students are enrolled. Show all your work, and provide a sentence explaining each step of your calculation