(a) The standard normal curve is graphed below. Shade the region under the standard normal curve to the left of z=0.50.

To shade the region under the standard normal curve to the left of $z = 0.50$, follow these steps:

Break Down the Problem

1. Understand that the standard normal curve represents a normal distribution with a mean of 0 and a standard deviation of 1.
2. Identify the value of $z$ given, which is $z = 0.50$.
3. Shade the area to the left of this $z$-score on the graph.

Relevant Concepts

1. The standard normal distribution is symmetric, and the area under the curve to the left of any $z$-score can be found using the cumulative distribution function (CDF) for the normal distribution.
2. The area to the left of $z = 0.50$ represents the probability that a standard normal random variable is less than 0.50.

Analysis and Detail

1. Look up the cumulative probability for $z = 0.50$ using a standard normal table or a calculator: $P(Z < 0.50) \approx 0.6915$
2. This indicates that approximately 69.15% of the distribution lies to the left of $z = 0.50$.

Verify and Summarize

1. Confirm that the $z$-score is correctly used to determine the shaded area.
2. The area under the curve to the left of $z = 0.50$ has been verified as approximately 69.15%.

Final Answer

The area shaded to the left of $z = 0.50$ under the standard normal curve represents about 69.15% of the distribution.