Let's go through each part of this question based on the provided image.

The problem describes the cholesterol levels of women as following a normal distribution with:

• Mean ($\mu$) = 188 mg/dL
• Standard deviation ($\sigma$) = 29 mg/dL

Part a)

The correct answer for drawing and labeling the Normal model is marked as C in the image. This figure represents the mean (188 mg/dL) in the center and marks each standard deviation interval (68%, 95%, and 99.7%) symmetrically around the mean.

Part b)

For this part, we are asked:

What percent of women do you expect to have cholesterol levels over 210 mg/dL?

To solve this:

1. Find the z-score for 210 mg/dL: $z = \frac{210 - 188}{29} = \frac{22}{29} \approx 0.76$

2. Use a z-table or calculator to find the probability for $z = 0.76$.

   • The probability for $z \leq 0.76$ is approximately 0.7764.
   • Since we want the percentage above 210 mg/dL, we calculate $1 - 0.7764 = 0.2236$, or 22.36%.

So, the answer is 22.36%.

Part c)

What percent of women do you expect to have cholesterol levels between 150 mg/dL and 170 mg/dL?

To solve this:

1. Calculate the z-score for 150 mg/dL: $z = \frac{150 - 188}{29} = \frac{-38}{29} \approx -1.31$

2. Calculate the z-score for 170 mg/dL: $z = \frac{170 - 188}{29} = \frac{-18}{29} \approx -0.62$

3. Use a z-table or calculator to find the probabilities:

   • For $z = -1.31$, the probability is approximately 0.0951.
   • For $z = -0.62$, the probability is approximately 0.2676.

4. Find the percentage of women between 150 mg/dL and 170 mg/dL: $0.2676 - 0.0951 = 0.1725$ So, the answer is approximately 17.25%.

If you need further details on any calculation or have more questions, feel free to ask!

Related Questions to Consider:

1. What is the probability of cholesterol levels being below 150 mg/dL?
2. How would the percentages change if the standard deviation was different?
3. What cholesterol level corresponds to the top 5% of women in this distribution?
4. How would you interpret a z-score of 1.5 in this context?
5. How can the Empirical Rule be applied to estimate probabilities without calculating exact values?

Tip:

Always remember that in a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. This can help you estimate probabilities quickly.