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To solve the problem in question 1, we can use the **z-score formula**, which helps determine the proportion of data points that fall below a certain value in a normal distribution.

The z-score formula is:

\[
z = \frac{X - \mu}{\sigma}
\]

Where:
- $ X $ is the price of the wooden bed ($1399),
- $ \mu $ is the mean price ($1300),
- $ \sigma $ is the standard deviation ($300).

### Step 1: Calculate the z-score
\[
z = \frac{1399 - 1300}{300} = \frac{99}{300} \approx 0.33
\]

### Step 2: Use the z-score table
From the standard normal distribution table, a z-score of 0.33 corresponds to a proportion of approximately **0.6293**.

This means that about **62.93%** of beds cost less than the price of the wooden bed.

Would you like more details or clarifications?

Here are 5 related questions to explore further:
1. What is the significance of the z-score in a normal distribution?
2. How would the proportion change if the standard deviation were larger?
3. Can we use the z-score formula to compare data from different distributions?
4. How do z-scores relate to percentiles in a data set?
5. What if the price of the wooden bed was below the mean—how would the z-score and interpretation change?

**Tip:** Always round your final answer according to the required precision, but keep intermediate values more accurate for better results!

A set of bed prices are normally distributed with a mean of 1300 dollars and a standard deviation of 300 dollars. A wooden bed has a price of 1399 dollars. What proportion of beds cost less than the price of the wooden bed? You may round your answer to four decimal places.

Learn how to calculate the proportion of bed prices below a given price using the z-score formula. This example involves a mean price of 1300 dollars, a standard deviation of 300 dollars, and a specific bed priced at 1399 dollars. Ideal for students studying normal distributions and z-scores in statistics.

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