The random variablex has the following continuous probability distribution in the range 0 < x < k – 4 (where k is a positive number) is shown in the coordinate plane with x on the horizontal axis. f(x) k - 1.5 3 k –4 What is the median of x?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![The random variable \( x \) has the following continuous probability distribution in the range \( 0 \leq x \leq k - 4 \) (where \( k \) is a positive number) is shown in the coordinate plane with \( x \) on the horizontal axis.
### Diagram Explanation:
- **Axes**: The horizontal axis represents the variable \( x \), and the vertical axis represents the function \( f(x) \).
- **Line Segment**:
- There is a horizontal line at the height \( \frac{k}{3} - 1.5 \) that extends from \( x = 0 \) to \( x = k - 4 \).
- The line indicates a constant probability density function over this interval.
- **Endpoints**: At \( x = k - 4 \), the line ends indicating the boundary of the probability distribution.
### Question:
What is the median of \( x \)?
*Answer box provided for input.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa714d614-78a6-4d97-b2db-18c7cb38b192%2F41b4b10b-a092-45c8-abe6-d84a86b25437%2Fjsmvzuf_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)