A standardized test given to 10,000 students had scores normally distributed. Al scored 648 . The mean was 518 and the standard deviation was 130 . About how many students scored below him? 5000 8400 3400 6480 none of these

To determine how many students scored below Al, we first need to calculate his z-score using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \(X\) is Al's score (648), - \(\mu\) is the mean score (518), - \(\sigma\) is the standard deviation (130). Plugging in the values: \[ z = \frac{(648 - 518)}{130} = \frac{130}{130} = 1 \] Next, we can use the z-score to find the percentage of students who scored below Al. A z-score of 1 corresponds to a percentile of approximately 84.13% in a standard normal distribution. To find the number of students who scored below Al, we can calculate: \[ \text{Number of students below Al} = \text{Total students} \times \text{Percentile} \] Given that there are 10,000 students: \[ \text{Number of students below Al} = 10,000 \times 0.8413 \approx 8413 \] Since we are looking for an approximate number, we can round this to 8400. Thus, the answer is **8400**.