csat-suneung 2023 Q28

csat-suneung · South-Korea · csat__math 4 marks Continuous Probability Distributions and Random Variables PDF Graph Interpretation and Probability Computation

A continuous random variable $X$ has a range of $0 \leq X \leq a$, and the graph of the probability density function of $X$ is as shown in the figure. When $\mathrm { P } ( X \leq b ) - \mathrm { P } ( X \geq b ) = \frac { 1 } { 4 }$ and $\mathrm { P } ( X \leq \sqrt { 5 } ) = \frac { 1 } { 2 }$, what is the value of $a + b + c$? (Here, $a$, $b$, and $c$ are constants.) [4 points]
(1) $\frac { 11 } { 2 }$
(2) 6
(3) $\frac { 13 } { 2 }$
(4) 7
(5) $\frac { 15 } { 2 }$

A continuous random variable $X$ has a range of $0 \leq X \leq a$, and the graph of the probability density function of $X$ is as shown in the figure.\\
When $\mathrm { P } ( X \leq b ) - \mathrm { P } ( X \geq b ) = \frac { 1 } { 4 }$ and $\mathrm { P } ( X \leq \sqrt { 5 } ) = \frac { 1 } { 2 }$, what is the value of $a + b + c$? (Here, $a$, $b$, and $c$ are constants.) [4 points]\\
(1) $\frac { 11 } { 2 }$\\
(2) 6\\
(3) $\frac { 13 } { 2 }$\\
(4) 7\\
(5) $\frac { 15 } { 2 }$

Paper Questions

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