Final answer:
The results from the student intelligence tests administered by the teachers, if following a normal distribution, would form a bell-shaped curve, indicating the majority of scores around the mean with fewer at the extremes.
Step-by-step explanation:
When Superintendent Hastings asked all teachers in the school district to administer student intelligence tests, if performances at each age level formed a normal distribution, the results were probably bell-shaped. This is because intelligence tests, like many human traits, tend to follow a bell curve, an indication of a normal distribution in a population. Therefore, if the conditions for a normal distribution are met, such as having a large and representative sample size, the natural outcome in the graph of such data is a bell-shaped curve, where the majority of students will score around the average, with fewer students scoring significantly below or above the average.