The image involves shading the region under the standard normal curve corresponding to a given normal distribution with $\mu = -2$ and $\sigma = 4$. The task asks for shading the probability of $X < 4$ under the standard normal curve.

Steps to Solve:

1. Convert the value $x = 4$ to a standard normal score (Z-score): The Z-score formula is: $Z = \frac{X - \mu}{\sigma}$ Substituting the given values:

   • $X = 4$, $\mu = -2$, and $\sigma = 4$, $Z = \frac{4 - (-2)}{4} = \frac{6}{4} = 1.5$

2. Interpret the Z-score: The value $Z = 1.5$ corresponds to the upper boundary of the shaded region under the standard normal curve.

3. Shade the region:

   • The shaded region will include all values to the left of $Z = 1.5$, starting from $Z = -\infty$ (left tail of the standard normal curve) and ending at $Z = 1.5$.

Conclusion:

To shade the corresponding region under the standard normal curve:

• Start shading from the far left ($Z = -\infty$) up to $Z = 1.5$.

Let me know if you'd like a detailed explanation on Z-scores, probabilities, or further clarification!

Related Questions:

1. What is the cumulative probability corresponding to $Z = 1.5$?
2. How do you convert between a normal distribution and the standard normal distribution?
3. What does the area under the normal curve represent?
4. How do you interpret Z-scores in real-world applications?
5. How do you find probabilities for values greater than $X$ instead of less than $X$?

Tip: Always standardize values to Z-scores when dealing with normal distributions and probability calculations!