Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Answer 1

Answer:

z = -0.4.

Step-by-step explanation:

Here's the formula for finding the z-score (a.k.a. standardized normal variable) of one measurement $x$ of a normal random variable $X \sim N(\mu,\; \sigma^{2})$:

$\displaystyle z = \frac{x-\mu}{\sigma}$,

where

• $z$ is the z-score of this measurement,
• $x$ is the value of this measurement,
• $\mu$ is the mean of the random normal variable, and
• $\sigma$ is the standard deviation (the square root of variance) of the random normal variable.

Let the length of a trout in this lake be $X$ inches.

$X \sim N(30, \; 4.5^{2})$.

• $\mu = 30$, and
• $\sigma = 4.5$.

For this measurement, $x = 28.2$. Apply the formula to get the z-score:

$\displaystyle z = \frac{x - \mu}{\sigma} = \frac{28.2 - 30}{4.5} = -0.4$.