Question

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

Answer 1

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.