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

Question

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?

查看解析

登录即可查看完整答案

类似问题

Question at position 48 IQs among undergraduates at Mountain Tech are approximately Normally distributed. The mean undergraduate IQ is about 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is about255151020

Question at position 46 If 30 is added to every number on a list, the only one of the following that is not changed isThe medianThe meanThe standard deviationThe 75th percentileThe mode

Question at position 9 ________ is a measure of dispersion that indicates how much the scores in a sample vary around the mean of the sample.RangeMedianCorrelation coefficientStandard deviation

TB MC Qu. 06-24 Of the following measures, the... Of the following measures, the best way to analyze the variability in the sample is to consider the:

位置24的问题 A stock had returns of 5 percent, 14 percent, 11 percent, −8 percent, and 6 percent over the past five years. What is the standard deviation of these returns?7.74%8.44%9.68%7.49%8.21%清除选择

A stock had returns of 16.15 percent, −6.15 percent, and 23.45 percent for the past three years. What is the standard deviation of the returns?

Let r=0.62, c=2.2 and m=1.2. Suppose that UC and UM are independent. What is the standard deviation of the point spread in the UBC game? Enter "999" if there is insufficient information to answer.

Suppose q=0.3. Then, the expected value of X is 2. What is the standard deviation of X?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单