H.) The following years of data are not included in the histogram above. Based o
ID: 3331823 • Letter: H
Question
H.) The following years of data are not included in the histogram above. Based on your analysis, estimate how many times in a 100 year period you expect discharges as large as those in the table below? Complete the table below. A probability table for high Z is at the end of your exam if you need it. Explain why you think this data was excluded. SHOW YOUR WORK ON THE FOLLOWING PAGE Number of expected Average July Discharge (cfs) occurrences in Year 100 years 1995 1998 1999 2006 2011 2435 2525 2939 2599 2024Explanation / Answer
This problem statement is incomplete. Please attach the following:
a) Histogram for normal rain: this is required to get the mean and standard deviation of the rain.
b) probability table for high values of Z: this is required to get the probability for high values of Z (beyond 3.5)
However, for the sake of this problem, I am going to assume that this information is given:
Normal distribution
mean = 200 cfs
standard deviation = 100 cfs
Please substitute the actual values as calculated from the histogram.
Using this information, we can calculate the probabilities:
Here is a sample calculation for 1995. Rainfall = 2435 cfs. Z-value = (2435 - 200) / 100 = 22.35
I will assume that as per the Z-table for huge Z, probability is 0.99999985. This means that probability of rain less than 2435 is 0.99999985. So, probability of rain > 2435 is 0.00000085 or 0.000085%. So, probability of this rain in 100 years = 100 * 0.000085% = 0.0085%.
In this fashion, we can fill in the table. Here are the steps:
1. Calculate Z value = (value in column 2 - mean) / standard deviation. For normal values, it is less than 3.5. However, in this case, it is expected to be greater than 3.5.
2. Calculate probability from the Z table for large values to get the probability. This should be higher than 0.9999 and smaller than 1.
3. Subtract this probability from 1 to get the probability of getting rain above that amount. This should be less than 0.0001 and greater than 0.
4. Multiply by 100 to get the expectation of that happening in 100 years. This should be less than 0.001 and greater than 0.
Explanation on why this data has been excluded:
If it can be demonstrated that this amount of rainfall is happening due to an uncommon external factor (like a hurricane) and does not happen when that factor does not happen (e.g. no hurricane in normal years), then we can exclude this data.
If we include this data, the results will be be skewed and will lead to incorrect interpretation.
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