Question

Anna caught a one-year-old flounder that was 145 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places. Anna's z-score is

Answer 1

Complete question:

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 126 with standard deviation of 23, and the mean length of two-year-old spotted flounder is 161 with a standard deviation of 27. The distribution of flounder lengths is approximately bell-shaped.

Anna caught a one-year-old flounder that was 145 millimeters in length. What is the z-score for this length? Round the answers to at least two decimal places. Anna's z-score is

Answer:

0.83

Step-by-step explanation:

Given:

For one year old:

Mean, u = 126

Standard deviation, $\sigma$ = 23

For two year old:

Mean, u = 161

Standard deviation, $\sigma$ = 27

Anna caught a one year old with length of 145. Ie, X = 145

Required: Find the Z score.

Take the Z score formula:

$Z = \frac{X - u}{\sigma}$

Substitute figures:

$Z = \frac{145 - 126}{23}$

$Z = \frac{19}{23}$

$= 0.826$

Approximately 0.823

Z score = 0.83