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Given that the variance of the numbers 1, 2, 3, 4, 5,..., 10 is 99/12, what is the standard deviation of the sequence 3, 6, 9, 12,..., 30?

1. 297/4
2. 3/2 √33
3. 3/2 √99
4. √(99/12)

Correct answer: 3/2 √33

Solution

The standard deviation of a set of numbers is proportional to the standard deviation of a related set of numbers when scaled. The sequence 3, 6, 9, 12,..., 30 is obtained by multiplying the original sequence by 3, which scales the standard deviation by the same factor, resulting in 3 times the standard deviation of the original sequence. Since the standard deviation of the original sequence is √(99/12), the standard deviation of the new sequence becomes 3 times that, leading to the correct option of 3/2 √33.

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