Find the mean and standard deviation for each uniform continuous model. (Round "Mean" answers to 1 decimal place and "Standard deviation" answers to 4 decimal places.) Mean standard deviation a. U(2, 12) b. U(90, 250) C. U(1, 93)
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!
![## Uniform Continuous Distribution: Mean and Standard Deviation
In this exercise, you are required to find the mean and standard deviation for each given uniform continuous model. Please follow the instructions to round your answers appropriately.
**Instructions:**
- **Mean:** Round answers to 1 decimal place.
- **Standard Deviation:** Round answers to 4 decimal places.
**Models:**
a. \( U(2, 12) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
b. \( U(90, 250) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
c. \( U(1, 93) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
**Explanation:**
1. **Uniform Continuous Distribution:** In a uniform continuous distribution, all outcomes are equally likely within the interval \([a, b]\).
2. **Mean Formula:** The mean for a uniform continuous distribution \( U(a, b) \) is calculated as:
\[
\text{Mean} = \frac{a + b}{2}
\]
3. **Standard Deviation Formula:** The standard deviation for a uniform continuous distribution \( U(a, b) \) is calculated using the formula:
\[
\text{Standard Deviation} = \sqrt{\frac{(b - a)^2}{12}}
\]
Please input your answers accordingly in the provided table. Once completed, click on "Check my work" to validate your responses.
Note: Ensure to follow the rounding instructions precisely to match the required format.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbcf5de3-296f-47d6-9d91-3d7cd8b6c4b2%2Fde21a012-4d75-419b-8dc0-01f76726544e%2Fevgo8rc_processed.jpeg&w=3840&q=75)
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