The image shows a problem involving a normal distribution with mean $\mu = -2$ and standard deviation $\sigma = 3$. The shaded region represents the probability of obtaining a value greater than 1. You're asked to shade the corresponding region under the standard normal curve (a normal distribution with $\mu = 0$ and $\sigma = 1$).

Steps to approach this:

1. Standardize the value: To find the corresponding region under the standard normal curve, we need to convert the value $x = 1$ to a z-score using the formula: $z = \frac{x - \mu}{\sigma}$ For this problem: $z = \frac{1 - (-2)}{3} = \frac{1 + 2}{3} = \frac{3}{3} = 1$ So, the z-score corresponding to $x = 1$ in this distribution is $z = 1$.

2. Shade the region: In the standard normal distribution, you would shade the area to the right of $z = 1$. This represents the probability of obtaining a value greater than 1 in the standard normal curve.

In the bottom graph, you need to shade the area from $z = 1$ to the right.

Would you like further details on how to calculate or interpret this probability?

Related questions:

1. What is the total area under a standard normal curve?
2. How do we interpret z-scores in real-world problems?
3. How can we use z-tables to find probabilities for normal distributions?
4. What is the probability of obtaining a value greater than 1 in this specific distribution?
5. How can you use the empirical rule to estimate probabilities in normal distributions?

Tip:

Remember that the total area under any normal distribution curve equals 1, representing the total probability.