Video Game	Total Sales in
Millions of
Units	Weeks
On List
Super Mario Bros. U for WiiU	1.7	78
NBA 2K14 for PS4	0.6	27
Battlefield 4 for PS3	0.9	29
Titanfall for Xbox One	1.2	10
Yoshi's New Island for 3DS	0.2	10
Use the sample of size five and Chebyshev's Rule to find the minimum percentage of total sales that are between 0.0046 million and 1.8354 million. (Round your answer to two decimal places.)

Chebyshev's Rule states that for any distribution, the proportion of data that lies within \(k\) standard deviations of the mean is at least \( \left(1 - \frac{1}{k^2}\right) \). To apply this, we need the mean and standard deviation of the data set, as well as the boundaries within which we are evaluating the proportion.

### Steps:

1. **Find the mean and standard deviation of the dataChebyshev's Rule states that for any distribution, the proportion of data that lies within \(k\) standard deviations of the mean is at least \( \left(1 - \frac{1}{k^2}\right) \). To apply this, we need the mean and standard deviation of the data set, as well as the boundaries within which we are evaluating the proportion.

### Steps:

1. **Find the mean and standard deviation of the **

The sales figures for the five games are:
\[
1.7, \ 0.6, \ 0.9, \ 1.2, \ 0.2
\]

- **Mean ( \( \mu \) ):**
\[
\mu = \frac{1.7 + 0.6 + 0.9 + 1.2 + 0.2}{5} = \frac{4.6}{5} = 0.92
\]

- **Variance and Standard Deviation ( \( \sigma \) ):**
\[
\text{Variance} = \frac{(1.7 - 0.92)^2 + (0.6 - 0.92)^2 + (0.9 - 0.92)^2 + (1.2 - 0.92)^2 + (0.2 - 0.92)^2}{5}
\]

Let's calculate this step-by-step.

The mean of the sales data is approximately \( 0.92 \) million units, and the standard deviation is approximately \( 0.51 \) million units.

2. **Determine the number of standard deviations for the given range:**

The range provided is between \( 0.0046 \) million and \( 1.8354 \) million units. Now, calculate how many standard deviations each boundary is away from the mean:

- Lower bound: \( 0.0046 \)
- Upper bound: \( 1.8354 \)

The number of standard deviations for each bound is given by:

\[
k_{\text{lower}} = \frac{0.92 - 0.0046}{0.51}, \quad k_{\text{upper}} = \frac{1.8354 - 0.92}{0.51}
\]

Let's compute these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk you through solving this manually, or assist you in another way?

Here are some related questions you may find helpful:
1. How is Chebyshev's Rule applied to different types of data?
2. What is the relationship between standard deviation and the mean in Chebyshev's Rule?
3. How does the percentage change when the range of sales data is wider?
4. What is the significance of the number of standard deviations from the mean?
5. How would the calculation change for a larger data set?

**Tip:** Chebyshev’s Rule applies to any distribution, not just normal ones, making it useful when the distribution shape is unknown.

Use the sample of size five and Chebyshev's Rule to find the minimum percentage of total sales that are between 0.0046 million and 1.8354 million. (Round your answer to two decimal places.)

This guide demonstrates how to apply Chebyshev's Rule to a sample of five video game sales data points, calculating the minimum percentage of sales between 0.0046 million and 1.8354 million units. Learn how to compute the mean, standard deviation, and apply statistical rules to estimate the data distribution. Suitable for undergraduate statistics students.

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