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The length of time required by students to complete a
Chapter 4, Problem 17E(choose chapter or problem)
The length of time required by students to complete a one-hour exam is a random variable with a density function given by
\(f(y)=\left\{\begin{array}{ll} c y^{2}+y, & 0 \leq y \leq 1, \\ 0, & \text { elsewhere. } \end{array}\right.\)
a Find c.
b Find \(F(y)\).
c Graph \(f(y)\) and \(F(y)\).
d Use \(F(y)\) in part (b) to find \(F(-1)\), \(F(0)\) and \(F(1)\).
e Find the probability that a randomly selected student will finish in less than half an hour.
f Given that a particular student needs at least 15 minutes to complete the exam, find the probability that she will require at least 30 minutes to finish.
Questions & Answers
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QUESTION:
The length of time required by students to complete a one-hour exam is a random variable with a density function given by
\(f(y)=\left\{\begin{array}{ll} c y^{2}+y, & 0 \leq y \leq 1, \\ 0, & \text { elsewhere. } \end{array}\right.\)
a Find c.
b Find \(F(y)\).
c Graph \(f(y)\) and \(F(y)\).
d Use \(F(y)\) in part (b) to find \(F(-1)\), \(F(0)\) and \(F(1)\).
e Find the probability that a randomly selected student will finish in less than half an hour.
f Given that a particular student needs at least 15 minutes to complete the exam, find the probability that she will require at least 30 minutes to finish.
Step 1 of 7
It is given that the random variable under consideration is the length of the time required to complete an one-hour exam.
The density function of the random variable is
\(f(y)=\left\{\begin{array}{ll} c y^{2}+y, & 0 \leq y \leq 1, \\ 0, & \text { elsewhere. } \end{array}\right.\)
Using this we need to find the required values.
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