Question

rainforest data

mean = 7 \quad \sigma^2 = 12.405 \quad \sigma \approx 3.522

when using the formula \\(z_x = \frac{x - \mu}{\sigma}\\) for the z-score for the 11.7 data point:

\\(x = \\) box, \\(\mu = \\) box

Explanation:

Identify the given values

We are given the following statistics from the rainforest data:

• \(\text{Mean} = 7\)
• \(\sigma^2 = 12.405\)
• \(\sigma \approx 3.522\)

We are also given a specific data point:

• \(\text{Data point} = 11.7\)

Map variables to the z-score formula

The z-score formula is:

$$ z_x = \frac{x - \mu}{\sigma} $$

where:

• \(x\) represents the specific data point value.
• \(\mu\) represents the population mean.
• \(\sigma\) represents the standard deviation.

Determine the values of x and \(\mu\)

Matching our given values to the variables:

• The data point is \(11.7\), so \(x = 11.7\).
• The mean is \(7\), so \(\mu = 7\).

Answer:

When using the formula \(z_x = \frac{x - \mu}{\sigma}\) for the z-score for the 11.7 data point, \(x =\) <blank>11.7</blank>, \(\mu =\) <blank>7</blank>.