Question 1201439
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Answers:
Mean = <font color=red size=4>10.5</font>
Standard Deviation = <font color=red size=4>2.87</font> (approximate)


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Explanation:


The number of tickets is a discrete variable. 
It can only be equal to one of the following whole numbers {6,7,8,9,10,11,12,13,14,15}
This random variable would be continuous if it made sense to have some fractional amount of tickets (eg: 6.785 tickets), but of course it doesn't make sense to have a fractional amount of tickets.


The mean of a discrete uniform random variable is found by adding up the endpoints, and then dividing in half. 
We are computing the midpoint.
midpoint = (a+b)/2
midpoint = (6+15)/2
midpoint = 21/2
midpoint = 10.5
<font color=red>The mean is 10.5</font>
It represents the center of the distribution.
The proof should be fairly straight-forward, but let me know if you need me to go into more detail in this regard.


The standard deviation of a discrete uniform random variable isn't as straight-forward.
The formula is
{{{s = sqrt(( (b-a+1)^2 - 1 )/12)}}}
One proof is found here
<a href = "https://proofwiki.org/wiki/Variance_of_Discrete_Uniform_Distribution">https://proofwiki.org/wiki/Variance_of_Discrete_Uniform_Distribution</a>


Plug in a = 6 and b = 15
{{{s = sqrt(( (b-a+1)^2 - 1 )/12)}}}


{{{s = sqrt(( (15-6+1)^2 - 1 )/12)}}}


{{{s = 2.87228132326901}}}


{{{s = 2.87}}}
<font color=red>The standard deviation is approximately 2.87</font>
The standard deviation is a measure how spread out a distribution is.


Side note:
Some textbooks will present the standard deviation formula as
{{{s = sqrt( (n^2-1)/12 )}}}
where n = b-a+1 represents the number of whole numbers from a to b, including both endpoints.
Example: {6,7,8} has n = b-a+1 = 8-6+1 = 3 items.
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