Final answer:
To find the probability of a catfish being between 35 cm and 40 cm, we convert the given lengths to z-scores and use a z-table to determine the probability associated with each z-score and subtract to find the final result, 4.22% in this case.
Step-by-step explanation:
The probability that a randomly chosen catfish has a length between 35 cm and 40 cm can be calculated using normal distribution properties. To solve this, we can convert the lengths into z-scores. The z-score for a length of 35 cm is (35 - 37) / 9 = -0.22, and for 40 cm it's (40 - 37) / 9 = 0.33. We then consult a z-table or use statistical software to find the probabilities corresponding to these z-scores and subtract them to find the probability that the length is between these values.
For example, if the z-table gives us a probability of 0.5871 for a z-score of -0.22 and 0.6293 for a z-score of 0.33, then the probability of the catfish length being between 35 cm and 40 cm is 0.6293 - 0.5871 = 0.0422 or 4.22%.