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If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

1. 3a² - 34a + 91 = 0
2. 3a² - 23a + 44 = 0
3. 3a² - 26a + 55 = 0
4. 3a² - 32a + 84 = 0

Correct answer: 3a² - 32a + 84 = 0

Solution

Mean = (16+a)/4. Variance = [sum (x-mean)^2]/4 = 12.25 simplifies to 3a^2 - 32a + 84 = 0 (roots a=14/3 and a=6).

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