Answer:
D. 2.81
Explanation:
To find the critical value that corresponds to a 99.5% confidence level, we follow the steps below.
Step 1: Subtract the confidence level from 100% to find the α level.
[tex]100\%-99.5\%=0.5\%[/tex]
Step 2: Convert the result from Step 1 to a decimal.
[tex]0.5\%=\frac{0.5}{100}=0.005[/tex]
Step 3: Divide Step 2 by 2 (this is called “α/2”) to find the area in each tail.
[tex]\frac{\alpha}{2}=\frac{0.005}{2}=0.0025[/tex]
Step 4: Subtract the result in Step 3 from 1. This is because we want the area in the middle, not the area in the tail.
[tex]1-0.0025=0.9975[/tex]
Step 5: Look up the area from Step in the z-table.
0.9975 comes up under 2.8+0.01 = 2.81
The value is 2.81
