A regular die is rolled n times. Let S_n be the total sum of the numbers showed up. Say without calculations what S_n is equal to on the average. For a > 0, let a⁺_n = 3.5n+a√n, a⁻_n = 3.5n − a√n, and q_n(a) = P(a⁻_n ≤ S_n ≤ a⁺_n). 

(a) Show that q_n(a) → q(a) as n → ∞, where q(a) is a finite function of a. Find q(a). 

(b) Estimate a for which q(a) = 0.9. 

(c) Proceeding from what you obtained, estimate z for which P(−z ≤ S₁₀₀ − 350 ≤ z) = 0.9.