AP Statistics : How to find the standard deviation of the sum of independent random variables
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Example Questions
Example Question #1 : How To Find The Standard Deviation Of The Sum Of Independent Random Variables
A high school calculus exam is administered to a group of students. Upon grading the exam, it was found that the mean score was 95 with a standard deviation of 12. If one student's z score is 1.10, what is the score that she received on her test?
108.2
110.1
105.3
109.2
107.2
108.2
The z-score equation is given as: z = (X - μ) / σ, where X is the value of the element, μ is the mean of the population, and σ is the standard deviation. To solve for the student's test score (X):
X = ( z * σ) + 95 = ( 1.10 * 12) + 95 = 108.2.
Example Question #133 : Statistical Patterns And Random Phenomena
First, find that 
Then find the mean and standard deviation of 
Example Question #134 : Statistical Patterns And Random Phenomena
Consider the discrete random variable 
-
with
-
with
-
with
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with
Compute the variance of the distribution.
The variance of a discrete random variable is computed as
for all the values of 
First, we compute 
So we have
Example Question #131 : Statistical Patterns And Random Phenomena
Clothes 4 Kids uses standard boxes to ship their clothing orders and the mean weight of the clothing packed in the boxes is 
Note that the weight of a packed box = weight of books + weight of box + weight of packing material used.
It is given that 
The calculation of the standard deviation of the weights of the packed boxes is
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