A die is rolled 24 times. Use the Central Limit Theorem to estimate the probability that a) the sum is greater than 84 b) the sum is equal to 84

a) Note that for a single roll, E(X) is = 1/6(1+2+3+4+5+6) = 3.5
And σ2 = E(X2) – {E(X)} 2
= 1/6(12 + 22 + 32 + 42 + 52+ 62) - 3.52 = 91/6 - 12.25 = 35/12
The sum S24 = S1 + S2 + … + S24 is a random variable.
Using above result, E (S24) = 24*3.5 = 84
And σ2 (S24) = 24*35/12 = 70
Hence...