Let's break down this problem:

Part (a)

The task is to shade the area under the standard normal distribution curve to the left of $z = 1.00$.

The standard normal curve is a symmetrical, bell-shaped curve centered at $z = 0$. The value $z = 1.00$ represents a point one standard deviation to the right of the mean. Shading the area to the left of $z = 1.00$ means shading the entire area from the far left (negative infinity) up to $z = 1.00$.

Part (b)

For this part, we need to find the area under the standard normal curve to the left of $z = 1.00$. This area represents the cumulative probability up to $z = 1.00$.

Using a standard normal distribution table or a calculator, the area to the left of $z = 1.00$ is approximately: $0.8413$ Thus, the answer for part (b) is $0.8413$.

Would you like a detailed explanation of how to use the standard normal table or additional information on the standard normal distribution?

Related Questions

1. What is the area under the standard normal curve to the left of $z = -1.00$?
2. How would the shaded region change if $z = -1.00$ instead of $z = 1.00$?
3. What is the area to the right of $z = 1.00$?
4. How is the standard normal distribution curve derived?
5. Why is the standard normal distribution curve symmetrical?

Tip

When using a standard normal table, always make sure to check if it gives cumulative probabilities from the left, as most tables do, to avoid misinterpretations.