To find the probability that a bottle contains between 12.17 and 12.23 ounces, we will use the properties of the normal distribution. Given:

• Mean ($\mu$) = 12.27 ounces
• Standard deviation ($\sigma$) = 0.06 ounces

We need to find the probability $P(12.17 \leq X \leq 12.23)$.

1. Convert the values 12.17 and 12.23 to their corresponding z-scores using the formula:

$z = \frac{X - \mu}{\sigma}$

For $X = 12.17$:

$z_1 = \frac{12.17 - 12.27}{0.06} = \frac{-0.10}{0.06} = -1.67$

For $X = 12.23$:

$z_2 = \frac{12.23 - 12.27}{0.06} = \frac{-0.04}{0.06} = -0.67$

2. Use the standard normal distribution table (or a calculator) to find the probabilities corresponding to these z-scores.

For $z = -1.67$:

$P(Z \leq -1.67) = 0.0475$

For $z = -0.67$:

$P(Z \leq -0.67) = 0.2514$

3. The probability that the bottle contains between 12.17 and 12.23 ounces is the difference between these probabilities:

$P(12.17 \leq X \leq 12.23) = P(Z \leq -0.67) - P(Z \leq -1.67) = 0.2514 - 0.0475 = 0.2039$

Therefore, the correct answer is:

$\boxed{0.2039}$

Would you like more details or have any questions?

Here are 5 numbered questions for you to ask:

1. How do you find z-scores for a given data set?
2. What is the significance of the standard normal distribution table?
3. How do you calculate probabilities for non-standard normal distributions?
4. What are some real-world applications of normal distribution?
5. How does changing the mean or standard deviation affect the normal distribution?

Tip: When dealing with normal distributions, always remember to convert raw scores to z-scores to utilize the standard normal distribution table effectively.