Chapter 11 - Probability and Calculus - 11.1 Continuous Probability Models - 11.1 Exercises - Page 576: 38

b) 0.3

We are given $2x$ for $0 \lt x \lt 1$ and $0$ otherwise The question gives the information that the probability that the insurance payment is less than 0.5 is equal to 0.64. To find C: $P(X-C\lt0.5)=(X\lt0.5 + C)=\int^{0.5+C}_{0}2xdx$ $=x^2|^{0.5+C}_{0}$ $=(0.5+C)^2-0$ $=C^2+C+0.25$ so $C^2+C+0.25=0.64$ $C^2+C-0.39$ $C=0.3$ or $C=-1.3$ Hence, the correct answer is $b)0.3$