Consider the amount of time taken by a wholesaler to fill an order, which follows a uniform distribution from three to six days. Drag and drop the parameters used in the uniform distribution against their corresponding values.

Drag and drop application.
3

3 drop zone empty.
4.5

4.5 drop zone empty.
0.87

0.87 drop zone empty.
0.33

0.33 drop zone empty.
Mean

Standard Deviation

Range

P(x)

For a uniform distribution, the parameters and their corresponding values are:

1. **Mean**: The average of the minimum (3) and maximum (6) values, calculated as \(\frac{3 + 6}{2} = 4.5\).

2. **Standard Deviation**: For a uniform distribution over \([a, b]\), the standard deviation is calculated as \(\frac{b - a}{\sqrt{12}}\). Here, \(a = 3\) and \(b = 6\), so the standard deviation is approximately 0.87.

3. **Range**: The difference between the maximum and minimum values, i.e., \(6 - 3 = 3\).

4. **P(x)**: The probability density function (PDF) for a uniform distribution is given by \(\frac{1}{b - a}\), which for this distribution is \(\frac{1}{6 - 3} = 0.33\).

So, the correct drag-and-drop matches would be:

- **Mean**: 4.5
- **Standard Deviation**: 0.87
- **Range**: 3
- **P(x)**: 0.33

Would you like more details or have any other questions?

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Here are five related questions to deepen your understanding:

1. How do you calculate the variance for a uniform distribution?
2. What would happen to the standard deviation if the range were increased?
3. How does a uniform distribution differ from a normal distribution in terms of probability?
4. Can a uniform distribution have negative values, and how would that affect the calculations?
5. How would you calculate the cumulative distribution function (CDF) for this uniform distribution?

**Tip**: In a uniform distribution, every outcome within the specified range is equally likely!

Consider the amount of time taken by a wholesaler to fill an order, which follows a uniform distribution from three to six days. Drag and drop the parameters used in the uniform distribution against their corresponding values.

Learn how to calculate key parameters of a uniform distribution for the time taken by a wholesaler to fill an order, ranging from 3 to 6 days. Includes step-by-step solutions for calculating the mean, standard deviation, range, and probability density function (PDF). Suitable for Grades 10-12.

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