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The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W = 7+2X. What are the mean and standard deviation of W?
A. The mean is 24, and the standard deviation is 6.
B. The mean is 24, and the standard deviation is 13.
C. The mean is 31, and the standard deviation is 3.
D. The mean is 31, and the standard deviation is 6.
E. The mean is 31, and the standard deviation is 13.

Sagot :

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Answer: D. The mean is 31, and the standard deviation is 6.

Step-by-step explanation:

Given the data :

X = mean = 12 ; Standard deviation = 3

W = 7 + 2x

Variance of W = 2x

Variance = Standard deviation²

(2x)² = 4x²

Variance

Standard deviation of X = 3

Variance (W) = 4*3² = 4 * 9 = 36

Variance (W) = 36

Standard deviation = sqrt(variance)

Standard deviation = sqrt(36) = 6

Mean ; of x = 12

Mean(W) = 7 + 2(12)

Mean = 7 + 24

Mean = 31

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