Question

SAT Critical Reading Scores Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed. 200<x<375 u=503 o=123 200 375 800 Score

Answer 1

Given that, mean (μ) = 503 and standard deviation $(\sigma)$ = 123

Using standard normal z-table we want to find, P(200 < X < 375)

Where, X ~ Normal (503, 123)

P(200 < X < 375) _P 200 - 503 X - = P123 = P(-2.46 <Z< -1.04) 375 - 503 1 23 = P(Z < -1.04) - P(Z < -2.46) = 0.1492 -0.0069 = 0.1423

Therefore, required probability is 0.1423