SHOW ALL WORK AND EXPLAIN YOUR ANSWER Example 3.26 Can we approximate poker winn
ID: 3074926 • Letter: S
Question
SHOW ALL WORK AND EXPLAIN YOUR ANSWER
Example 3.26 Can we approximate poker winnings by a normal distribution? We consider the poker winnings of an individual over 50 days. A histogram and normal probability plot of these data are shown in Figure 3.13. The data are very strongly right skewed in the histogram, which corresponds to the very strong deviations on the upper right component of the normal probability plot. If we compare these results to the sample of 40 normal observations in Example 3.24, it is apparent that these data show very strong deviations from the normal model.Explanation / Answer
First one:
The data set is too small to see the clear structure in the histogram.
The normal probability plot is also the same, where there are some deviations from the line. However, these deviations are not strong.
So, not normal distribution.
Second one:
The second one shows diagnostic plots for the data set with 100 simulated observations. The histogram shows more normality and the normal probability plot shows a better fit. While there is one observation that deviates noticeably from the line, it is not particularly extreme.
Third one:
The third one with 400 observations has a histogram that greatly resembles the normal distribution, while the normal probability plot is nearly a perfect straight line.
In the normal probability plot, there is one observation (the largest and in top of figure) that deviates slightly from the line. If that observation had deviated 3 times further from the line, it would be of much greater concern in a real data set. Apparent outliers can occur in normally distributed data but they are rare.
Note:
The histograms look more normal as the sample size increases, and the normal probability plot becomes straighter and more stable.
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