Final answer:
To find the percentage of women in the active group who were at or below their pre-pregnancy weight at 12 months postpartum, we need to use the concept of the normal distribution. We have the mean weight loss of 12 pounds and the standard deviation of 3 pounds. Approximately 0.0032% of women in the active group were at or below their pre-pregnancy weight at 12 months postpartum.
Step-by-step explanation:
To find the percentage of women in the active group who were at or below their pre-pregnancy weight at 12 months postpartum, we need to use the concept of the normal distribution. We have the mean weight loss of 12 pounds and the standard deviation of 3 pounds. First, we need to standardize the weight loss by calculating the z-score using the formula: z = (x - μ) / σ, where x is the weight loss, μ is the mean, and σ is the standard deviation. We want to find the percentage of women at or below their pre-pregnancy weight, so we need to find the cumulative probability from the standard normal distribution table for the z-score. Finally, we can convert the cumulative probability to a percentage by multiplying by 100.
Let's assume that x is the weight loss of a woman in the active group at 12 months postpartum. We want to find P(x <= 0), where 0 is the weight loss for being at or below the pre-pregnancy weight. Using the z-score formula, we can calculate: z = (0 - 12) / 3 = -4. We can then find the cumulative probability for the z-score -4 using a standard normal distribution table, which is approximately 0.000032.
To convert the cumulative probability to a percentage, we multiply by 100: 0.000032 * 100 = 0.0032%. Therefore, approximately 0.0032% of women in the active group were at or below their pre-pregnancy weight at 12 months postpartum.