**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.**

**Part: 0 / 3**

**0 of 3 Parts Complete**

The person has spent at least 

$14,000

P(x>14000)

To solve $ P(x > 14000) $, we need to find the probability that the financial loss $ x $ is greater than $14,000. Given:

- The mean $ \mu = 23943 $
- The standard deviation $ \sigma = 3000 $

We can calculate the $ z $-score using the formula:
\[
z = \frac{x - \mu}{\sigma}
\]

### Step 1: Calculate the $ z $-score for $ x = 14000 $
\[
z = \frac{14000 - 23943}{3000}
\]
\[
z = \frac{-9943}{3000} \approx -3.3143
\]

### Step 2: Find $ P(z > -3.3143) $
On the TI-83/84 calculator, go to:
1. `2nd` -> `DISTR` -> `normalcdf(`.
2. Enter the bounds for $ z $: `normalcdf(-3.3143, ∞)`. Since the calculator doesn't allow ∞, use a large positive number (e.g., 10).
3. Input the mean $ 0 $ and standard deviation $ 1 $.

The probability $ P(z > -3.3143) $ should return approximately **0.9994**.

Thus:
\[
P(x > 14000) \approx 0.9994
\]

Would you like details on the steps, or do you have any questions?

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### Related Questions
1. What is $ P(x < 20000) $ for this distribution?
2. How would we find $ P(x > 25000) $?
3. What is the probability that a randomly selected person spent between $20,000 and $30,000 on their divorce?
4. What does the probability $ P(x > 14000) \approx 0.9994 $ imply in practical terms?
5. How would changes in the standard deviation affect the probability $ P(x > 14000) $?

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**Tip:** When using the TI-83/84, remember that normalcdf(lower bound, upper bound, mean, standard deviation) is the format for finding probabilities under a normal curve.

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.

Part: 0 / 3

0 of 3 Parts Complete

The person has spent at least $14,000

P(x>14000)

Discover how to calculate the probability that financial losses in a divorce exceed $14,000 using a normal distribution. Given an average loss of $23,943 and a standard deviation of $3000, this example uses the z-score formula and a TI-83 Plus/TI-84 Plus calculator for step-by-step guidance. Ideal for college-level statistics students.

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