Final answer:
To find the z-value with 99.76% area to its right in the normal distribution, one uses a z-table or a calculator function like invNorm(0.0024,0,1), looking for an area to the left of 0.0024, indicating a z-value more negative than -2.326.
Step-by-step explanation:
To find the z-value that has 99.76% of the area under the standard normal curve to its right, we need to find a value such that the area to the left is 0.0024 (1 - 0.9976). Using a z-table, statistical software, or a calculator with inverse cumulative normal distribution functions, we can determine this z-value.
For example, using the TI-83, 83+, or 84+ calculator, one would use the command invNorm(0.0024,0,1) to find this value. Alternatively, using a standard normal probability table, we look for the closest area to 0.0024 in the inside part of the table and identify the corresponding z-value.
The value given as z0.01, which has the property where 0.01 is to the right and 0.99 to the left, is 2.326. But we are looking for an even smaller area to the right, implying a z-value that is more extreme. If the area to the left of z (the larger portion) is 0.0024, we find a more negative z-score. Hence, the z-value we are interested in is less than -2.326.