Question

rainforest data: mean = 7 $sigma^{2}=12.405$ $sigmaapprox3.522$ when using the formula $z_{x}=\frac{x - mu}{sigma}$ for the z - score for the 11.7 data point: $x = 11.7$; $mu = 7$ $z_{11.7}approx1.3$ is 11.7 within a z - score of 3? yes because $z_{11.7}<3$. yes because $z_{11.7}=3$. no because $z_{11.7}>3$.

Explanation:

Step1: Identify values for formula

$x = 11.7$, $\mu=7$, $\sigma\approx3.522$

Step2: Calculate z - score

$z_{11.7}=\frac{x - \mu}{\sigma}=\frac{11.7 - 7}{3.522}=\frac{4.7}{3.522}\approx1.3$

Step3: Compare z - score with 3

Since $1.3<3$, 11.7 is within a z - score of 3.

Answer:

Yes because $z_{11.7}<3$.