Statistics (12th Edition)

Published by Pearson

Chapter 5 - Continuous Random Variables - Exercises 5.1 - 5.19 - Learning the Mechanics - Page 229: 5.6a

3

Work Step by Step

$P(x \geq a) = 0.5$ $P(x \geq a) = ∫_{a}^{∞} f(x).dx$ = $∫_{a}^{∞} \frac{1}{d-c}.dx$ = $∫_{a}^{∞} \frac{1}{2}.dx$ = $∫_{a}^{4} \frac{1}{2}.dx +$∫_{4}^{∞} \frac{1}{2}.dx$= 1/2 (4-a) + 1/2 (0)= (4-a)/2 Since$P(x \geq a) = 0.5\$ (4-a)/2 = 0.5 4-a = 1 a = 3

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