Final Answer:
The area under the standard normal curve between z = -0.82 and z = 2.11 is approximately 0.8186.
Step-by-step explanation:
To find the area under the standard normal curve between two z-values, you'll want to use a graphing calculator like the TI-84 and its built-in normalcdf function. For this case, the standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.
To calculate this using the TI-84 calculator:
1. Turn on the calculator and press the "2ND" key followed by "VARS" to access the DISTR menu.
2. Choose "2: normalcdf" for the cumulative distribution function.
3. Input the lower bound, -0.82, as the first parameter, and the upper bound, 2.11, as the second parameter.
4. Press "ENTER" to obtain the area under the curve between these z-values.
The normalcdf function provides the cumulative probability from the lower z-value to the upper z-value. For this problem, it gives the area under the standard normal curve between z = -0.82 and z = 2.11, which represents the probability that a randomly selected value from a standard normal distribution falls within that range. Rounding the answer to four decimal places, the calculated area is approximately 0.8186, representing the probability or area under the curve in the specified range.