To find the probability that a bottle contains between 12.01 and 12.15 ounces, we will again use the properties of the normal distribution. Given:

• Mean ($\mu$) = 12.11 ounces
• Standard deviation ($\sigma$) = 0.05 ounces

We need to find the probability $P(12.01 \leq X \leq 12.15)$.

1. Convert the values 12.01 and 12.15 to their corresponding z-scores using the formula:

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

For $X = 12.01$:

$z_1 = \frac{12.01 - 12.11}{0.05} = \frac{-0.10}{0.05} = -2$

For $X = 12.15$:

$z_2 = \frac{12.15 - 12.11}{0.05} = \frac{0.04}{0.05} = 0.8$

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

For $z = -2$:

$P(Z \leq -2) = 0.0228$

For $z = 0.8$:

$P(Z \leq 0.8) = 0.7881$

3. The probability that the bottle contains between 12.01 and 12.15 ounces is the difference between these probabilities:

$P(12.01 \leq X \leq 12.15) = P(Z \leq 0.8) - P(Z \leq -2) = 0.7881 - 0.0228 = 0.7653$

Therefore, the correct answer is:

$\boxed{0.7654}$

Would you like more details or have any questions?

Here are 5 numbered questions for you to ask:

1. How do you interpret the z-score in a normal distribution?
2. What is the role of the standard deviation in the normal distribution?
3. How do you find probabilities for values outside the given range in a normal distribution?
4. How can you apply the normal distribution to quality control in manufacturing?
5. What are the steps to find probabilities for any normal distribution problem?

Tip: Always ensure to use the standard normal distribution table or appropriate statistical software for precise probability calculations.