Final answer:
The grades on the math exams are categorized based on the number of standard deviations from the mean.
Step-by-step explanation:
The subject of this question is Mathematics. The grades are based on a curve, where scores are categorized according to how many standard deviations they are from the mean. The mean grade on Rachel's math exam was 74, with a standard deviation of five. Rachel earned an 80, which falls within one standard deviation above the mean, so her grade would be a C. Similarly, the mean grade on Becca's exam was 47, with a standard deviation of two. Becca earned a 51, which also falls within one standard deviation above the mean, making her grade a C. Lastly, the mean grade on Matt's exam was 70, with a standard deviation of eight. Matt earned an 83, which falls within one standard deviation above the mean, so his grade would be a C.