6.) For women, in European sizes, the mean size shoe size is 38.46 with a standard deviation of 1.84. The
conversion to US sizes is given by USsize = EuroSize × 0.7865 – 22.5.
 a.) [4 pts.] What is the mean women’s shoe size for these respondents in US units?
 b.) [4 pts.] What is the standard deviation in US units? 

Let's break down the problem step by step:

### a.) Finding the mean women’s shoe size in US units:

The mean European shoe size is given as 38.46. To find the mean US shoe size, we can apply the conversion formula:

\[
\text{US size} = \text{Euro size} \times 0.7865 - 22.5
\]

Substituting the mean European size:

\[
\text{Mean US size} = 38.46 \times 0.7865 - 22.5
\]

Now we can compute this value:

\[
\text{Mean US size} = 30.24579 - 22.5 = 7.74579
\]

Thus, the mean US shoe size is approximately **7.75**.

### b.) Finding the standard deviation in US units:

The standard deviation in European sizes is given as 1.84. To find the standard deviation in US sizes, we use the conversion factor \(0.7865\) because standard deviation is affected only by the multiplicative factor, not by the constant subtraction:

\[
\text{Standard deviation in US units} = 1.84 \times 0.7865
\]

Let's calculate this:

\[
\text{Standard deviation in US units} = 1.44676
\]

Thus, the standard deviation in US shoe sizes is approximately **1.45**.

---

### Summary of Results:
- **Mean US shoe size** = 7.75
- **Standard deviation in US units** = 1.45

Would you like more details or further explanation on any part?

Here are 5 related questions:
1. How would the calculation change if the standard deviation was doubled?
2. What is the conversion formula for men's shoe sizes in this case?
3. How would we calculate the variance in US units?
4. Can the same method be applied to other regions like UK shoe sizes?
5. How is the impact of constant subtraction on mean different from its impact on standard deviation?

**Tip**: When converting between units, remember that multiplication affects both mean and standard deviation, while addition or subtraction only affects the mean.

6.) For women, in European sizes, the mean size shoe size is 38.46 with a standard deviation of 1.84. The conversion to US sizes is given by USsize = EuroSize × 0.7865 – 22.5. 
 a.) What is the mean women’s shoe size for these respondents in US units? 
 b.) What is the standard deviation in US units?

This page provides a detailed solution for converting European women's shoe sizes to US sizes, calculating the mean size (7.75) and standard deviation (1.45) based on a given formula. Perfect for students in Grades 10-12 learning about unit conversions and statistics.

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