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The mean number of books read

last year by a group of students is
normally distributed with a mean of 10
and a standard deviation of 6. If Austin
is 0.5 standard deviations below the mean
and Kaleigh is 2 standard deviations
above the mean, how many more books
did Kaleigh read than Austin?


1 Answer

4 votes

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.

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