When calculating probabilities associated with normal distributions, [b]z-scores[/b] are used to standardize and compare scores from different distributions. [br][list][*]A z-score for a particular value measures the number of standard deviations away from the mean. [br][/*][*]A positive z-score corresponds to a value that is above the mean, and a negative z-score corresponds to a value that is below the mean. [br][/*][*]The letter z is used to represent a variable that has a [b]standard normal distribution[/b] where the mean is 0 and standard deviation is 1. [br][/*][*]The formula for calculating a z-score for any value x with standard deviation σ and mean μ is [math]z=\frac{x-\mu}{\sigma}[/math].[br][/*][/list]The U.S. Department of Agriculture (USDA), in its Official Food Plans (www.cnpp.usda.gov), states that the average cost of food for a 14- to 18-year-old [b]male[/b] is $261.50 per month. Assume that the monthly food cost for a 14- to 18-year-old male is approximately normally distributed with a mean of $261.50 and a standard deviation of $16.25. The USDA also states that the average cost of food for a 14- to 18-year-old [b]female[/b] is $215.20 per month. Assume that the monthly food cost for a 14- to 18-year-old female is approximately normally distributed with a mean of $215.20 and a standard deviation of $14.85. [br][br]Use z-scores to compare Billy, who spends $270 a month on food, with Gina, who spends $250 a month on food.