To find the area/probability to the left of k in a normal distribution,

To find the area/probability to the left of k in a normal distribution,

use normalcdf(k, 1EE99,
)

use normalcdf(a, b,
)

use normalcdf(-1EE99, k,
)

use invNorm(k decimal,
)

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.

To find the area/probability to the left of k in a normal distribution, use normalcdf(k, 1EE99), use normalcdf(a, b), use normalcdf(-1EE99, k), use invNorm(k decimal, ).

Learn how to calculate the area or probability to the left of a value k in a normal distribution using key functions like normalcdf and invNorm. This guide covers cumulative distribution functions and their applications in normal probability calculations.

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