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Lucy scored a 45 on her statistics exam and wants to know how she did relative to her zoology

exam, which she scored a 47 on, but they were out of a different number of points. The class
average for the statistics exam was 39 with a standard deviation of 4. The class average for the
zoology exam was 41 with a standard deviation of 2. Which exam did Lucy score higher on?

User TLE
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1 Answer

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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!

User JillevdW
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