Answer:
To answer this question, we need to compare Lucy's scores on both exams using a common scale, such as the z-score. The z-score tells us how many standard deviations a score is above or below the mean. A higher z-score means a better performance relative to the class average. To calculate the z-score, we use the formula:
z = (x - mu) / sigma
where x is the score, mu is the mean, and sigma is the standard deviation. Plugging in the numbers for the statistics exam, we get:
z = (45 - 39) / 4
z = 1.5
This means Lucy scored 1.5 standard deviations above the mean on the statistics exam. Now let's do the same for the zoology exam:
z = (47 - 41) / 2
z = 3
This means Lucy scored 3 standard deviations above the mean on the zoology exam. Wow, Lucy is a zoology whiz! Comparing the two z-scores, we can see that Lucy scored higher on the zoology exam than on the statistics exam, even though her raw score was only 2 points higher. This is because the zoology exam had a lower mean and a lower standard deviation, making Lucy's score more impressive.
So, to summarize, Lucy did better on the zoology exam than on the statistics exam, according to the z-scores. Maybe she should consider switching her major to zoology, or at least take more classes in that field. She clearly has a knack for it. Or maybe she just got lucky and guessed well on some questions. Either way, good job Lucy!