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Rainforest data:

Mean: [tex]7[/tex]
[tex]\sigma^2 = 12.405[/tex]
[tex]\sigma \approx 3.522[/tex]

When using the formula [tex]z_x = \frac{x - \mu}{\sigma}[/tex] for the [tex]z[/tex]-score for the 11.7 data point:

[tex]x = \square[/tex]
[tex]\mu = \square[/tex]

Sagot :

GinnyAnsweridn
To find the z-score for the data point 11.7 using the given rainforest data, we need to follow these steps:

1. Identify the given data:
- Mean ([tex]\(\mu\)[/tex]) = 7
- Variance ([tex]\(\sigma^2\)[/tex]) = 12.405
- Standard deviation ([tex]\(\sigma\)[/tex]) ≈ 3.522
- Data point ([tex]\(x\)[/tex]) = 11.7

2. Z-score formula:
[tex]\[ z_x = \frac{x - \mu}{\sigma} \][/tex]

3. Substitute the known values into the formula:
[tex]\[ \mu = 7 \][/tex]
[tex]\[ \sigma ≈ 3.522 \][/tex]
[tex]\[ x = 11.7 \][/tex]

4. Perform the calculation:
[tex]\[ z_x = \frac{11.7 - 7}{3.522} \][/tex]

Therefore, the z-score ([tex]\(z_x\)[/tex]) for the data point 11.7 is:

[tex]\[ z_x ≈ 1.334 \][/tex]

So, when using the formula for the z-score and given this rainforest data:
- [tex]\( x = 11.7 \)[/tex]
- [tex]\( \mu = 7 \)[/tex]

And this results in a z-score of:

[tex]\[ z_x ≈ 1.334 \][/tex]
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