Question

The weight of frogs in grams in a marsh population are normally distributed with mean (μ) equal to 23.5 grams and standard deviation (σ) equal to 1.2 gram. What is the probability that a randomly selected frog weighs between 22 and 25 grams?

Answer 1

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.