A large data set is approximately normally distributed. Three values in the data set are represented by a, b, and c where a is the value of the third quartile, b is the value with a -score of 1, and c is the value of the 70th percentile. List a, b, and c

To order the values a, b, and c—where: - \( a \) is the third quartile (Q3, which corresponds to the 75th percentile), - \( b \) is the value with a z-score of 1, - \( c \) is the value at the 70th percentile— you can use the following relationships based on the properties of a normal distribution: 1. **Third Quartile (Q3)**: The third quartile corresponds to the 75th percentile. This means Q3 is greater than 70% of the data. 2. **Z-score of 1**: A z-score of 1 indicates that this value is one standard deviation above the mean. In a standard normal distribution, about 84.13% of data points fall below this z-score, meaning the z-score of 1 is greater than the 70th percentile (which corresponds to a z-score of approximately 0.524). 3. **70th Percentile**: This value, denoted as \( c \), is less than Q3 (the 75th percentile) but greater than the mean. Based on this information, we can rank the values: - The 70th percentile (\( c \)) is the smallest. - The z-score of 1 (\( b \)) comes next, as it represents a value higher than the 70th percentile. - The third quartile (\( a \)) is the largest, as it signifies the 75th percentile. Thus, we can list them in order: **c < b < a**.