Question

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 126 with standard deviation of 18, and the mean length of two-year-old spotted flounder is 162 with a standard deviation of 28. The distribution of flounder lengths is approximately bell-shaped. Anna caught a one-year-old flounder that was 150 millimeters in length. What is the z-score for this length?

Answer 1

The z-score for Anna's one-year-old flounder that measures 150 millimeters in length is approximately 1.33, indicating that the flounder is 1.33 standard deviations longer than the mean length for one-year-old spotted flounder.

Step-by-step explanation:

The z-score is a statistic that measures the number of standard deviations a given data point is from the mean. To calculate the z-score for Anna's one-year-old flounder that measures 150 millimeters in length, we use the following formula:

Z = (X - μ) / σ

Where X is the value of the data point, μ (mu) is the mean, and σ (sigma) is the standard deviation. For the one-year-old spotted flounder, the mean (μ) is 126 millimeters and the standard deviation (σ) is 18 millimeters.

Following the formula:

Z = (150 - 126) / 18 = 24 / 18 ≈ 1.33

Therefore, the z-score for the one-year-old flounder that Anna caught is approximately 1.33.