Let's analyze the question parts provided in your homework.

Part (a)

The correct choice for drawing and labeling the Normal model is option C. This option shows the Normal distribution centered at the mean of 196 mg/dL with standard deviations of 28 mg/dL marked correctly, covering 68%, 95%, and 99.7% of the data within ±1, ±2, and ±3 standard deviations, respectively. This choice aligns with the given mean and standard deviation.

Part (b)

To find the percentage of women expected to have cholesterol levels over 200 mg/dL, we can use the properties of the Normal distribution.

1. Calculate the z-score for 200 mg/dL: $z = \frac{X - \mu}{\sigma} = \frac{200 - 196}{28} = \frac{4}{28} \approx 0.14$

2. Find the cumulative probability associated with $z = 0.14$ using a standard Normal table or calculator:

   • The cumulative probability for $z = 0.14$ is approximately 0.5557. This represents the probability of cholesterol levels being below 200 mg/dL.

3. Calculate the probability of cholesterol levels being above 200 mg/dL: $P(X > 200) = 1 - P(X < 200) = 1 - 0.5557 = 0.4443$

4. Convert to percentage: $0.4443 \times 100 \approx 44.43\%$

So, the answer to part (b) is approximately 44.43%.

Would you like further clarification on any part? Here are five additional questions to expand your understanding:

1. How do we interpret the z-score in the context of the Normal distribution?
2. What are other methods to find probabilities in Normal distributions without tables?
3. How does changing the mean or standard deviation affect the shape of the Normal curve?
4. Why do we subtract the cumulative probability from 1 to find the probability of values above a certain point?
5. Can we apply this Normal model approach to any dataset?

Tip: When working with Normal distributions, it’s helpful to sketch the distribution and label key areas based on standard deviations for quick visual reference.