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The first of two samples has 100 items with mean 15 and standard deviation 3. The combined group of 250 items has mean 15.6 and standard deviation sqrt(13.44). Which of the following are correct? (A) Mean of second group is 16 (B) Mean of second group is 18 (C) Standard deviation of second group is 4 (D) Standard deviation of second group is 5

1. (A) Mean of second group is 16
2. (B) Mean of second group is 18
3. (C) Standard deviation of second group is 4
4. (D) Standard deviation of second group is 5

Correct answer: (A) Mean of second group is 16

Solution

n2=150. Combined mean: 15.6=(100*15+150*x2)/250 => x2=16 (A correct, B wrong). Combined variance: 13.44=[100*(9+0.36)+150*(sigma2²+0.16)]/250 => sigma2²=16, sigma2=4 (C correct, D wrong).

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