Final answer:
To find the probability of a frog weighing between 22 and 25 grams in a normally distributed population with mean 23.5 grams and standard deviation 1.2 grams, we calculate the z-scores for 22 and 25 grams and refer to the standard normal distribution to find the corresponding probabilities.
Step-by-step explanation:
The question is asking about the probability that a randomly selected frog weighs between 22 and 25 grams when the weights of frogs are normally distributed with a mean (μ) of 23.5 grams and a standard deviation (σ) of 1.2 grams. To find this probability, we can use z-scores to standardize the weights and then refer to the standard normal distribution table.
First, calculate the z-scores for 22 and 25 grams:
- z for 22 grams = (22 - 23.5) / 1.2 = -1.25
- z for 25 grams = (25 - 23.5) / 1.2 = 1.25
Next, look up these z-scores in the standard normal distribution table to find the corresponding probabilities. The probability that lies between these two z-scores reflects the probability that a frog weighs between 22 and 25 grams. Add these probabilities together to find the total probability.
Note that you would need a z-table or technology to find the exact probabilities associated with the z-scores. The key idea is to understand the concept of using the standard normal distribution to compute probabilities for a normal distribution with any mean and standard deviation.