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.