Find the area under the standard normal distribution curve to the left of z = - 0.82. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to
at least four decimal places.
The area to the left of the z value is

To find the area under the standard normal distribution curve to the left of \( z = -0.82 \) using a TI-83 Plus or TI-84 Plus calculator, follow these steps:

1. Turn on the calculator and press the **2nd** key, followed by the **VARS** key to access the distribution menu.
2. Choose **2:normalcdf(**. This is the cumulative distribution function for the normal distribution.
3. Input the following values:
   - **Lower bound**: Since we want the area to the left of \( z = -0.82 \), use a large negative number (e.g., -1E99 or -9999) as the lower bound.
   - **Upper bound**: Enter \( -0.82 \) as the upper bound.
   - **Mean**: The mean for the standard normal distribution is 0.
   - **Standard deviation**: The standard deviation is 1.
4. The input should look like this: `normalcdf(-1E99, -0.82, 0, 1)`.
5. Press **Enter** to get the result.

The calculator will give you the area to the left of \( z = -0.82 \), which is approximately:

\[
0.2061
\]

Thus, the area to the left of \( z = -0.82 \) is approximately **0.2061**.

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you calculate the area to the right of a given z-value using the TI-84 calculator?
2. What is the significance of the area under the standard normal curve in probability?
3. How can you calculate z-scores given a data point, mean, and standard deviation?
4. How does the TI-84 calculate the cumulative area under the normal curve?
5. Can you use the normalcdf function to find probabilities between two z-values?

**Tip:** When using a standard normal table, always ensure to check whether it gives the area to the left or right of the z-value to avoid confusion.

Find the area under the standard normal distribution curve to the left of z = -0.82. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.

Discover how to calculate the area under the standard normal distribution curve to the left of z = -0.82 using a TI-83 Plus/TI-84 Plus calculator. This solution walks through the key steps, applying the normalcdf function, with the final area approximately 0.2061. Suitable for high school students studying statistics or probability.

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