Let's address each part of the question and analyze the correct graphs:

Part a) $z > -1.4$

This asks for the area of the normal distribution to the right of $z = -1.4$.

• In a standard normal distribution, the curve is symmetric with a mean of 0.
• A vertical line would be drawn at $z = -1.4$ (which is to the left of the mean), and the area to the right of $z = -1.4$ should be shaded.

The correct option should have shading on the right side of $z = -1.4$, which corresponds to option C.

Part b) $z < -1.9$

This asks for the area to the left of $z = -1.9$.

• We would expect a vertical line at $z = -1.9$, and the area to the left of this line will be shaded.
• Since this is less than $z = -1.9$, the shading would cover the leftmost portion of the graph, including the tail.

Part c) $0.85 < z < 1.85$

This asks for the area between $z = 0.85$ and $z = 1.85$.

• In this case, we would draw two vertical lines: one at $z = 0.85$ and one at $z = 1.85$, and shade the area between these two values.
• This will be a small section of the distribution, located to the right of the mean (since both values are positive).

Part d) $|z| < 0.6$

This refers to the area where the absolute value of $z$ is less than 0.6, meaning the area between $z = -0.6$ and $z = 0.6$.

• This would involve drawing vertical lines at $z = -0.6$ and $z = 0.6$ and shading the area between them.
• The shaded region is around the mean (0), covering a portion close to the center of the normal curve.

Would you like me to calculate the exact percentages for these regions and provide the correct graphical representation as well?

Related Questions:

1. What does the area under a normal distribution curve represent?
2. How do you calculate the percentage of a region using the Z-table?
3. What is the total area under a standard normal curve?
4. Why is the normal distribution symmetric around the mean?
5. How do you find the cumulative probability for a given Z-value?

Tip: The total area under a standard normal curve is always 1 (or 100% probability), and Z-scores represent the number of standard deviations from the mean.