If SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325, find the probability that a randomly selected SAT score is between 1550 and 1575.

A.

0.5714

B.

0.9684

C.

0.0316

D.

0.5398

Mean, x_bar = 1518

Standard deviation, sigma = 325

Range required: 1550 ≤ X ≤ 1575

Z = (X - x_bar) / sigma

Z1 = (1550-1518) / 325 ≈ 0.1

Z2 = (1575-1518) / 325 ≈ 0.18

From Z tables,

P (Z1) = 0.5398

P (Z2) = 0.5714

P (1550≤X≤1575) = P (Z2) - P (Z1) = 0.5714 - 0.5398 = 0.0316

The correct answer is C.