Math Problem Statement
Financial Burden for a Divorce The average amount of financial losses in a divorce is $23,943, according to one survey. Assume that the variable is approximately normally distributed and the standard deviation is $3000. If a randomly selected divorced person is chosen, find the probabilities. Use a TI-83 Plus/TI-84 Plus calculator and round the answers to at least four decimal places. p(x>14000)=
Solution
To find the probability where is normally distributed with a mean and standard deviation , you can use the following steps:
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Calculate the Z-score:
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Use the Z-score to find the probability: On a TI-83/TI-84 calculator, use the command: Alternatively, find using:
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Calculate: Using the calculator:
Thus, .
Would you like more details on any part of this process? Here are some related questions you might consider:
- How do you calculate the Z-score for different values?
- What is the significance of the standard deviation in this context?
- How can you interpret the probability result?
- What are other factors that can influence financial losses in a divorce?
- How would this probability change with a different mean or standard deviation?
Tip: Always double-check your calculator settings to ensure you're using the normal distribution functions correctly!
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Probability
Formulas
Z = (X - μ) / σ
P(X > a) = 1 - P(Z < (a - μ) / σ)
Theorems
Central Limit Theorem
Properties of Normal Distribution
Suitable Grade Level
Grades 10-12
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