Question

calculating a z - score
one study of 91 bald eagle eggs found that the eggs had a mean length of 73.6 millimeters and standard deviation of 2.9 millimeters.
one of the bald eagle eggs found was 74.9 millimeters long.
which is closest to the z - score for the egg?
-0.45
0.45
1.02
1.30

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Plug in given values

Substitute $x=74.9$, $\mu=73.6$, $\sigma=2.9$ into the formula:
$z = \frac{74.9 - 73.6}{2.9}$

Step3: Calculate numerator first

$74.9 - 73.6 = 1.3$

Step4: Compute final z-score

$z = \frac{1.3}{2.9} \approx 0.45$

Answer:

0.45