For some value of p, we have E[X]=11.2 and Var[X]=50.56. What is the standard deviation of (-4)*X?

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BlackTom AI · Accepted Answer

This question asks for the standard deviation of a scaled random variable, specifically (-4) * X.
First, recall that for any random variable X and constant a, the standard deviation transforms as SD(aX) = |a| * SD(X). The mean E[X] is not needed here, since standard deviation depends on the spread (variance), not on the mean.
Next, we use Var[X] = 50.56, so SD(X) = sqrt(Var[X]) = sqrt(50.56).
Compute sqrt(50.56): since 7.11^2 = 50.5521, the exact value is slightly less than 7.11; a closer approximation is 7.11056 (to five decimals), giving SD(X) ≈ 7.11056.
Now apply the scaling: SD((-4) * X) = | -4 | * SD(X) = 4 * 7.11056 ≈ 28.44224.
Rounding this to four decimal places yields 28.4422, and to two decimal places 28.44.
The provided answer 28.4800 corresponds to a slightly larger SD(X) (approximately 7.12) and may reflect a different rounding convention or a small arithmetic discrepancy. However, based on Var[X] = 50.56, the standard computation gives about 28.4422.
In summary, the exact approach is: SD((-4)X) = 4 * sqrt(50.56) ≈ 28.4422, and any close rounding should align with that value within the chosen precision.

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Final Exam - TUE Dec 09 2025 - Requires Respondus LockDown Browser

For some value of p, we have E[X]=11.2 and Var[X]=50.56. What is the standard deviation of (-4)*X?

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