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You already demonstrated that you know Chebyshev's Theorem in the other problem, so i think might have misread the problem.
The budget is $350K, but the mean expenditure is $390K. The variance is 10^8 dollars squared, which means the standard deviation is $10K. Chebyshev's theorem says to allow twice the standard deviation for 75%. Hence, $390K ± $20K seems correct.
I don't read anywhere where it says that the mean expenditure is $390k. Perhaps, I need to add $40000 to $350k but why should I do it? I think I don't understand the question statement. Please help me with it. Thanks.
I don't read anywhere where it says that the mean expenditure is $390k. Perhaps, I need to add $40000 to $350k but why should I do it? I think I don't understand the question statement. Please help me with it. Thanks.
I agree that you dont' understand the question. I mentioned this in my post above.
The problem is asking about the "actual expenditure". Hence, the budget number is irrelevant. The problem clearly stated that the actual expenditure always exceeds the estimates and the mean excess is $40K. Hence, you must add the average excess to the budget.
Q1: Could you please help me with this query? Kindly just let me know if my answers are correct. Thanks.
Q2: It would really kind of you if you could help me with this query.
Q3: Could you please help me with this query too? Though this problem is not important, I'm just curious to understand what is being done in the solution. Thank you.
Q2: I'm not entirely sure how the definition of "collectively exhaustive" applies in this case, but based on how I interpret it, the group of categrories doesn't seem exhaustive to me. For example, a caucasian male that never worked because he inherited money at an early age does not fit the categories. Such a person has a phone, money to spend and people to talk to. Although that category might have far fewer people than the other categories, it only requires finding one person in North Carolina that fits this description to prove that the categories are not collectively exhaustive. A larger group might be white college students that haven't entered the work force yet. Such people are destined to be professionals and white collar workers, but they aren't yet.
As you noted, the budget was only approved at full amount once in 20 years. So, what probability would you assign to this year's budget being approved at the full amount?
By the way, this is a very good example of why you need to apply statistics very carefully. Surely, a straight assignment of this year's probabilities based on a 20 year history is not going to be accurate. Perhaps it's the best one can do, but I doubt that. An expert can assign probabilities based on current information much better in this case.
For example, most likely the year that the budget was fully approved was a year when there was a strong drive among politicians and citizens to spend money on military. If the policitical climate has changed, an expert may well know that the chance of approving a full budget is absolutely zero. In such a case, using a 5% probability based on past history is ridiculous.
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