Questions: 1. z Scores Professional football quarterback Tom Brady is 193 cm tall. Based on statistics for the males from Data Set 1 "Body Data" in Appendix B, his height converts to the z score of 2.66. How many standard deviations is his height above the mean?

1. z Scores Professional football quarterback Tom Brady is 193 cm tall. Based on statistics for the males from Data Set 1 "Body Data" in Appendix B, his height converts to the z score of 2.66. How many standard deviations is his height above the mean?
Transcript text: 1. $z$ Scores Professional football quarterback Tom Brady is 193 cm tall. Based on statistics for the males from Data Set 1 "Body Data" in Appendix B, his height converts to the $z$ score of 2.66 . How many standard deviations is his height above the mean?
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Solution

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Solution Steps

Step 1: Understanding the Z-Score

The z-score is a statistical measure that describes a value's relationship to the mean of a group of values. It is calculated using the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where:

  • \( z \) is the z-score,
  • \( X \) is the value,
  • \( \mu \) is the mean of the distribution,
  • \( \sigma \) is the standard deviation of the distribution.
Step 2: Given Information

In this case, Tom Brady's height corresponds to a z-score of \( z = 2.66 \). This indicates that his height is \( 2.66 \) standard deviations above the mean height of the population.

Step 3: Conclusion

Thus, we conclude that Tom Brady's height is \( 2.66 \) standard deviations above the mean.

Final Answer

\(\boxed{2.66}\)

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