Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of 2.71. Round your answer to one decimal place. inches Submit Question

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Problem Statement**

Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of 2.71. Round your answer to one decimal place.

**Solution**

To solve this problem, use the formula for calculating the value from a z-score:

\[
\text{Height} = \text{Mean} + (\text{Z-score} \times \text{Standard Deviation})
\]

Given:
- Mean height = 69.0 inches
- Standard deviation = 2.8 inches
- Z-score = 2.71

Substitute the given values into the formula:

\[
\text{Height} = 69.0 + (2.71 \times 2.8)
\]

Calculate the height:

\[
\text{Height} = 69.0 + 7.588 = 76.588
\]

Round to one decimal place:

\[
\text{Height} = 76.6 \text{ inches}
\]

**Answer**

The height of a man with a z-score of 2.71 is 76.6 inches. 

**Note**
This problem involves understanding z-scores in statistics, which indicate how many standard deviations an element is from the mean.
Transcribed Image Text:**Problem Statement** Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of 2.71. Round your answer to one decimal place. **Solution** To solve this problem, use the formula for calculating the value from a z-score: \[ \text{Height} = \text{Mean} + (\text{Z-score} \times \text{Standard Deviation}) \] Given: - Mean height = 69.0 inches - Standard deviation = 2.8 inches - Z-score = 2.71 Substitute the given values into the formula: \[ \text{Height} = 69.0 + (2.71 \times 2.8) \] Calculate the height: \[ \text{Height} = 69.0 + 7.588 = 76.588 \] Round to one decimal place: \[ \text{Height} = 76.6 \text{ inches} \] **Answer** The height of a man with a z-score of 2.71 is 76.6 inches. **Note** This problem involves understanding z-scores in statistics, which indicate how many standard deviations an element is from the mean.
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