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A group of adult males has foot lengths with a mean of 28.36 cm and a standard deviation of 1.34 cm . Use the range rule of thumb for identifying significant values significantly low or significantly high. Is the adult male foot length of 25.2 cm significantly low or significantly high? Explain. Significantly low values are 25.68 cm or lower. (Type an integer or a decimal. Do not round.) Significantly high values are \( \square \mathrm{cm} \) or higher. (Type an integer or a decimal. Do not round.)

Ask by Bowers Blake. in the United States
Jan 22,2025

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Answer

Significantly high values are **31.04 cm** or higher.

Solution

To determine the **significantly high** foot length using the range rule of thumb, follow these steps: 1. **Calculate the Threshold for Significantly High Values:** \[ \text{Significantly High} = \text{Mean} + 2 \times \text{Standard Deviation} \] \[ \text{Significantly High} = 28.36\, \text{cm} + 2 \times 1.34\, \text{cm} = 28.36\, \text{cm} + 2.68\, \text{cm} = 31.04\, \text{cm} \] 2. **Interpretation:** - **Significantly Low Values:** 25.68 cm or lower. - **Significantly High Values:** **31.04 cm** or higher. 3. **Assessing 25.2 cm:** Since 25.2 cm is **lower** than 25.68 cm, it is considered a **significantly low** foot length. **Final Answer:** Significantly high values are **31.04** cm or higher.

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To find the significantly high values, we can use the range rule of thumb, which suggests that any value higher than the mean plus two standard deviations is considered significantly high. Let's calculate it: Mean = 28.36 cm Standard Deviation = 1.34 cm So, significantly high values are calculated as: 28.36 cm + 2 * 1.34 cm = 28.36 cm + 2.68 cm = 31.04 cm. Thus, significantly high values are 31.04 cm or higher. As for the foot length of 25.2 cm, it's indeed significantly low because it is below the threshold of 25.68 cm. So, this foot length is well below the average and is classified as significantly low. In summary: Significantly high values are 31.04 cm or higher. Significantly low values are 25.68 cm or lower.

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