Section 1
Describe the distribution of the number of wins using n=10000 and the probability of winning $1 from game A from your output , Calculate the mean and standard deviation, use wolfram alpha to find the 0th, 0.15th, 2.5th, 15.87th, 84,13th, 97.5th, 99.85th and 100th percentiles and find the percentiles of these values , Also find the predicted 0.15th, 2.5th, 15.87th, 84,13th, 97.5th, 99.85th percentiles using X=mean+Z×standarddeviation using the following approximate percentiles of the z distribution
|
|
Z
|
|
0.15th percentile z distribution
|
-3
|
|
2.5h percentile z distribution
|
-2
|
|
15.87th percentile z distribution
|
-1
|
|
84.13th percentile z distribution
|
1
|
|
97.5th percentile z distribution
|
2
|
|
99.85th percentile z distribution
|
3
|
SECTION 2
Redo the following just change the values of X and P(X) so they match the values in your assignment. and update the calculations , you have to find the mean and standard deviation of game A and find the standard error of the sample mean when n=4
Gambling game A has distribution
µ = 1×0.8-1×0.2=0.6
σ = √((1-0.6)2×0.8+ (-1-0.6)2×0.2) = 0.8
If you are getting the average of 4 plays then the standard error is σ/√n=0.8/√4=0.4
One application of this is that if you are going to find many sample averages µ predicts the average of the sample averages and the standard error predicts the standard deviation of many averages.
Section 3
Your data set has 4 different lists of results for 4 different cases,Each of the number represents a profit
Complete the following for all 4 cases use
www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php
to find the mean of and standard deviation and complete the following table
|
|
Which percentile
|
X profit
( this is just the number given on the output)
|
Z=(X-mean)/standard deviation
|
|
min
|
0th
|
|
|
|
Q1
|
25th
|
|
|
|
median
|
50th
|
|
|
|
Q3
|
75th
|
|
|
|
Max
|
100th
|
|
|
Section 4
Give a discussion of the results in section 3, So give a discussion of the range, interquartile range and z score, the discussion of z score does not have to be that detailed, for example if something is not unusual what is its z score close to?
Section 5
Use the results in section 3 and 4 to compare the profit of gambling game A to gambling game B and compare the small casino to a large casino, Note that you have the mean and standard deviation of profit so you want the average to be high and the standard deviation to be low
Section 6
Paraphrase the following, rewrite the following using your own words.
mean , standard deviation and percentiles are useful for working out what is common (what usually happens) and what is unusual (what rarely happens) .
If something is unusually low then it is the 0th percentile or close to the 0th percentile and it will be many standard deviations below average.
For example if an observation has a z score of -3 or a value even further from 0 such as -4 , -5 etc
The observation must be unusually low and only a few observations or none of the observations will be lower than the value.
If something is unusually high then it is the 100th percentile or close to the 100th percentile and it will be many standard deviations above average.
For example if an observation has a z score of 3 or a value even further from 0 such as 4 , 5 etc
The observation must be unusually high and only a few observations or none of the observations will be higher than the value.
Standard deviation measures the spread and there are many different reasons to measure spread. Examples
*investors want the spread to be low (they want low risk)
*Some gamble sometimes because they enjoy risk so they want the spread to be high
*You want the spread of an estimate to be low (this means it has low standard deviation and is more accurate)
Attachment:- tutorial group.rar