Final answer:
Tomijia is in the 70th percentile of her class test scores. By arranging the scores and calculating her rank, we determined that she scored higher than 70 percent of her classmates.
Step-by-step explanation:
To determine which percentile Tomijia is in based on her score on the standardized test, we must first understand what a percentile means. A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls. For example, the 70th percentile is the value below which 70 percent of the observations may be found.
The dataset provided includes ten scores: 42, 44, 56, 71, 74, 83, 89, 90, 90, 92. Tomijia scored an 89. To find her position in the dataset, we arrange the scores in ascending order and determine her rank among her peers. Since her score is the seventh highest, it surpasses the scores of six of her classmates.
To find the percentile rank, we use the formula:
Percentile Rank = (Number of values below the score + 0.5) / Total number of scores × 100
Following this formula, Tomijia's percentile rank would be:
((6 + 0.5) / 10) × 100 = (6.5 / 10) × 100 = 65th percentile
But since percentiles are typically reported in terms of 10s (e.g., 60th, 70th), we round up to the nearest 10th percentile. Therefore, Tomijia is in the 70th percentile, meaning she scored higher than 70 percent of her classmates.\
Thus, the correct option in the final part is the 70th percentile.