(b) Calculate the z-score for the largest value and interpret it in terms of standard deviations. Do the same for the smallest value. Round your answers to two decimal places. The largest value: z-score = \( \square \) The maximum of \( 39.5 \% \) obese is \( \square \) standard deviations \( \square \) the mean. The smallest value: z-score = \( \square \) i The minimum of \( 23.0 \% \) obese is \( \square \) i standard deviations \( \square \) the mean. eTextbook and Media

To calculate the z-scores for the largest and smallest values, you first need the mean and standard deviation of your data set. The z-score is calculated using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the value for which you're calculating the z-score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. Assuming from your data: - Largest value \( (X) = 39.5\% \) - Smallest value \( (X) = 23.0\% \) - Mean \( (\mu) \) and standard deviation \( (\sigma) \) will need to be known for precise calculations. Once you have these: 1. Plug the largest value into the formula to find its z-score: \( z = \frac{(39.5 - \mu)}{\sigma} \) 2. Do the same for the smallest value: \( z = \frac{(23.0 - \mu)}{\sigma} \) Since I don't have specific values for the mean and standard deviation, I can't provide exact z-scores or their interpretations. However, once calculated, the z-score indicates how many standard deviations the specific value is away from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below. For simulation: - Suppose you found the mean \( \mu = 31.0\% \) and standard deviation \( \sigma = 4.5\% \). - For the largest value: - \( z = \frac{(39.5 - 31.0)}{4.5} \approx 1.89 \) - The maximum of \( 39.5\% \) obese is approximately \( 1.89 \) standard deviations above the mean. - For the smallest value: - \( z = \frac{(23.0 - 31.0)}{4.5} \approx -1.78 \) - The minimum of \( 23.0\% \) obese is approximately \( 1.78 \) standard deviations below the mean. Feel free to ask more if you would like to dive deeper into z-scores or any other statistical concepts!