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.