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The problem refers to monthly mortgage payments with the following parameters:

- **Mean** $ \mu = 982 $ dollars
- **Standard deviation** $ \sigma = 180 $ dollars
- The distribution is **normally distributed**, and the question asks to find probabilities based on this information.

### Part (a) More than $1410
The probability given for $ X > 1410 $ is already stated as:
\[ P(X > 1410) = 0.0090 \]

### Part (b) Between $690 and $1240
We need to find:
\[ P(690 < X < 1240) \]

To solve this:
1. **Standardize** the values using the Z-score formula:
   \[
   Z = \frac{X - \mu}{\sigma}
   \]
2. Calculate Z-scores for $690 and $1240:
   \[
   Z_1 = \frac{690 - 982}{180} = \frac{-292}{180} \approx -1.622
   \]
   \[
   Z_2 = \frac{1240 - 982}{180} = \frac{258}{180} \approx 1.433
   \]
3. Using the **Standard Normal Distribution Table** (or Z-table), we find the probabilities for the Z-scores:
   - For $ Z_1 = -1.622 $, the probability is approximately $ P(Z_1) \approx 0.0525 $.
   - For $ Z_2 = 1.433 $, the probability is approximately $ P(Z_2) \approx 0.9236 $.

4. Finally, subtract the smaller probability from the larger one:
   \[
   P(690 < X < 1240) = P(Z_2) - P(Z_1) = 0.9236 - 0.0525 = 0.8711
   \]

Thus, the probability is approximately **0.8711**.

---

Would you like a detailed explanation on any of these steps? 

### Related Questions:
1. How do you calculate Z-scores for values outside the mean?
2. How does the normal distribution help in mortgage payment predictions?
3. What are the uses of the Standard Normal Distribution Table in probability?
4. How is probability linked to real-world financial decisions like mortgages?
5. What is the significance of calculating probabilities between two payment values?

### Tip:
Always round intermediate Z-scores and final probability answers to at least four decimal places to maintain accuracy.

Find the probabilities of monthly mortgage payments, where the average mortgage payment is $982, the standard deviation is $180, and the distribution is normally distributed. The questions ask for the probability of a payment being (a) more than $1410 and (b) between $690 and $1240.

Learn how to calculate the probability of monthly mortgage payments using the normal distribution. This problem covers finding probabilities for payments more than $1410 and between $690 and $1240. With a mean of $982 and a standard deviation of $180, apply Z-scores and the Standard Normal Distribution Table.

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