Final answer:
Kaleigh read 15 more books than Austin. Austin read 7 books and Kaleigh read 22 books, calculated using their positions in terms of standard deviations from the mean.
Step-by-step explanation:
To calculate how many more books Kaleigh read than Austin, first determine the number of books each one read. Since the mean number of books read is 10 and the standard deviation is 6, we can find the number of books each student read by using their respective standard deviation positions from the mean.
Austin is 0.5 standard deviations below the mean, so:
- Austin's number of books = Mean - (0.5 × Standard Deviation) = 10 - (0.5 × 6) = 10 - 3 = 7 books
Kaleigh is 2 standard deviations above the mean, so:
- Kaleigh's number of books = Mean + (2 × Standard Deviation) = 10 + (2 × 6) = 10 + 12 = 22 books
Now, subtract the number of books Austin read from the number Kaleigh read:
Kaleigh's books - Austin's books = 22 books - 7 books = 15 books
Therefore, Kaleigh read 15 more books than Austin.