In a normal distribution, finding the area (or probability) to the left of a value $k$ is related to the cumulative distribution function (CDF). Let's clarify the different commands you've mentioned:

1. normalcdf(k, 1EE99): This command calculates the area between $k$ and an extremely large positive number ($1 \times 10^{99}$), which represents the upper tail of the distribution. It gives the probability from $k$ to infinity, not the area to the left of $k$.

2. normalcdf(a, b): This calculates the area between two values $a$ and $b$ in a normal distribution. It finds the probability of a value falling between those two points.

3. normalcdf(-1EE99, k): This is the correct method to find the area to the left of $k$ in a normal distribution. The command calculates the probability from $-\infty$ (represented by $-1 \times 10^{99}$) to $k$, which is the cumulative probability up to $k$.

4. invNorm(k decimal): This command is used when you have a known probability and want to find the corresponding $z$-value (or $k$-value) for a normal distribution. For example, if you want the value where the cumulative probability is $0.95$, you would use invNorm(0.95).

Summary:

To find the area/probability to the left of a value $k$, you should use:

• normalcdf(-1EE99, k).

Would you like further details or explanations? Here are five questions to expand on this:

1. How do you calculate probabilities between two values in a normal distribution?
2. What is the difference between using normalcdf and invNorm?
3. How is the z-score related to probabilities in a normal distribution?
4. What does the $1 \times 10^{99}$ value represent in these commands?
5. How do you interpret a probability result from invNorm?

Tip: In a normal distribution, the mean is the center, and values further away (positive or negative) are less likely. Use the standard normal table for quick $z$-score lookups.