how would i use normalcdf() to get the answer

The `normalcdf()` function on a calculator, such as a TI-84, can be used to find the proportion of observations within a specified range of a normal distribution. For the standard normal distribution, the syntax is:

\[ \text{normalcdf(lower bound, upper bound)} \]

The lower and upper bounds are the z-scores you're interested in.

### A. Proportion where \( z > -1.66 \)
To find the proportion of observations where \( z > -1.66 \), you would enter:

\[ \text{normalcdf(-1.66, } \infty \text{)} \]

Since calculators don't use \( \infty \), you can substitute a very large positive number (e.g., 9999):

\[ \text{normalcdf(-1.66, 9999)} \]

This will give you the proportion directly. The result will be approximately **0.9515**.

### B. Proportion where \( -1.66 < z < 2.85 \)
To find the proportion of observations where \( -1.66 < z < 2.85 \), you would enter:

\[ \text{normalcdf(-1.66, 2.85)} \]

This will give you the proportion directly. The result will be approximately **0.9493**.

Would you like to know more about using `normalcdf()` or have any other questions?

Here are some related questions that might interest you:

1. How do you calculate the probability using `normalcdf()` for a non-standard normal distribution?
2. What is the inverse of `normalcdf()` and when would you use it?
3. How do you interpret the results from `normalcdf()` in context?
4. How does the `normalcdf()` function work internally?
5. What are the differences between `normalcdf()` and `normalpdf()`?

**Tip:** Always ensure that your calculator is set to use standard normal distribution (mean 0, standard deviation 1) when using `normalcdf()` with z-scores.

Learn how to use the normalcdf() function on a calculator to find proportions within specified ranges of a normal distribution. Includes examples such as finding proportions where z > -1.66 and -1.66 < z < 2.85.

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