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]
