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.

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