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For this problem, let's break it down into two parts as requested:

### Part (a)
You are asked to shade the region under the standard normal curve to the left of \( z = -1.50 \). This involves highlighting the area to the left of that point on the curve. This shaded area represents the probability that a randomly chosen value from a standard normal distribution is less than or equal to \( z = -1.50 \).

### Part (b)
To find the area under the standard normal curve to the left of \( z = -1.50 \), we can use a standard normal table or a calculator. Looking up the value of \( z = -1.50 \) in the table, we get:

\[
P(Z \leq -1.50) \approx 0.0668
\]

So, the area to the left of \( z = -1.50 \) is approximately \( 0.0668 \).

Would you like more details on how to use the standard normal table or how these values are computed?

Here are some follow-up questions to expand on this topic:
1. What is the interpretation of the area under the normal curve in a probability context?
2. How would the area change if you used a \( z \)-score of \( -1.00 \) instead of \( -1.50 \)?
3. Can you explain how to convert a raw score to a \( z \)-score in the context of a normal distribution?
4. What would be the area to the right of \( z = -1.50 \) on the standard normal curve?
5. How is the cumulative distribution function (CDF) used in finding probabilities related to the standard normal distribution?

**Tip:** Remember that the total area under the standard normal curve is always equal to 1, which represents the entire probability space.

Shade the region under the standard normal curve to the left of z = -1.50 and find the area using a standard normal table or calculator.

Learn how to find the area under the standard normal curve to the left of z = -1.50 using a Z-table or calculator. This problem explains how to shade the region and determine the cumulative probability, giving an answer accurate to four decimal places.

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