Let f(x) = k(x^2 + x) for 0 ≤ x ≤ 2 and 0 otherwise. (a) Find k. (b) Compute P(0.5 ≤ X ≤ 1.5).

k = 3/14 and P(0.5 ≤ X ≤ 1.5) = 25/56 ≈ 0.44643

k = 14/3 and P(0.5 ≤ X ≤ 1.5) = 56/25 because the student inverted the normalization incorrectly

k = 3/14 and P(0.5 ≤ X ≤ 1.5) = 75/84 which is approximately 0.8929 if a student forgot to reduce the fraction fully and double-counted the k factor

k = 3/14 and P(0.5 ≤ X ≤ 1.5) = 0.5 since the interval is centered in the support and probabilities are symmetric