**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)=

To find the probability $ P(X > 14000) $ where $ X $ is normally distributed with a mean $ \mu = 23943 $ and standard deviation $ \sigma = 3000 $, you can use the following steps:

1. **Calculate the Z-score**:
   \[
   Z = \frac{X - \mu}{\sigma} = \frac{14000 - 23943}{3000} \approx -3.3143
   \]

2. **Use the Z-score to find the probability**:
   On a TI-83/TI-84 calculator, use the command:
   \[
   1 - \text{normalcdf}(-\infty, -3.3143)
   \]
   Alternatively, find $ P(Z < -3.3143) $ using:
   \[
   \text{normalcdf}(-3.3143, \infty)
   \]

3. **Calculate**:
   Using the calculator:
   \[
   P(X > 14000) \approx 1 - P(Z < -3.3143) \approx 0.0005
   \]

Thus, $ P(X > 14000) \approx 0.0005 $.

Would you like more details on any part of this process? Here are some related questions you might consider:

1. How do you calculate the Z-score for different values?
2. What is the significance of the standard deviation in this context?
3. How can you interpret the probability result?
4. What are other factors that can influence financial losses in a divorce?
5. 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!

The average amount of financial losses in a divorce is $23,943. 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)=.

Discover how to calculate the probability of financial losses in divorce scenarios, using a mean of $23,943 and a standard deviation of $3,000. This detailed guide explains the Z-score method and provides a step-by-step solution for p(X > 14000). Ideal for high school students studying statistics.

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