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Distances for students from centrally located college

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Please help with the following problem.

A college is located in the geographic center of mainland United States. The admission officer examines the east-west distance of the college from the hometown of each incoming resident student. Incoming resident students living to the east of the college are scored as + distances, and incoming resident students living to the west of the college are scored as - distances. She finds distance to be normally distributed around a mean of 0.00 miles (the college's location) and a standard deviation of 163 miles. Incoming resident student Carl DeMeo lives 216 miles west of the college.

What percentage of incoming resident students live
(a) in the same town as, or west of, Carl?
(b) east of Carl?
(c) between the college and Carl?

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This solution helps with a question involving distances for students from a centrally located college. Step by step calculations are provided.

Solution Preview

mu = 0, sigma = 163, x = -216

z = (x - mu)/sigma

z = (-216 - 0)/163 = -1.3251

(a) P(x <= -216) ...

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