Attention span in a population of students in a 50 minute class are found to be uniformly distributed with the given probability density function: {6 f(x) = { 10≤x≤50 otherwise a) What must c be equal to for this to be a valid probability density function? b) Determine the mean and median attention span of the students. c) Determine the standard deviation of the attention span of the students.
Attention span in a population of students in a 50 minute class are found to be uniformly distributed with the given probability density function: {6 f(x) = { 10≤x≤50 otherwise a) What must c be equal to for this to be a valid probability density function? b) Determine the mean and median attention span of the students. c) Determine the standard deviation of the attention span of the students.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
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![**Uniform Distribution and Attention Span**
In a study of student attention spans during a 50-minute class, it was found that the attention spans are uniformly distributed according to the following probability density function:
\[
f(x) =
\begin{cases}
c & \text{for } 10 \leq x \leq 50 \\
0 & \text{otherwise}
\end{cases}
\]
**Tasks:**
a) **Determine the Value of \( c \):**
- What must \( c \) be equal to, for this to be a valid probability density function?
b) **Calculate the Mean and Median:**
- Determine the mean and median attention span of the students.
c) **Calculate the Standard Deviation:**
- Determine the standard deviation of the attention span of the students.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F416064f9-c57b-46ee-9b50-14b257515654%2Fe5a36d0c-3776-4ce0-a324-cd19980577a1%2Fjdxs6m6_processed.png&w=3840&q=75)
Transcribed Image Text:**Uniform Distribution and Attention Span**
In a study of student attention spans during a 50-minute class, it was found that the attention spans are uniformly distributed according to the following probability density function:
\[
f(x) =
\begin{cases}
c & \text{for } 10 \leq x \leq 50 \\
0 & \text{otherwise}
\end{cases}
\]
**Tasks:**
a) **Determine the Value of \( c \):**
- What must \( c \) be equal to, for this to be a valid probability density function?
b) **Calculate the Mean and Median:**
- Determine the mean and median attention span of the students.
c) **Calculate the Standard Deviation:**
- Determine the standard deviation of the attention span of the students.
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