Question

complete the following table.
click here to view page 1 of the standard normal table.
click here to view page 2 of the standard normal table.
(type integers or decimals rounded to two decimal places as needed.)

Explanation:

Step1: Find the corresponding values for \(z_{0.10}\)

Using the standard normal table, for a right - tail area of \(0.10\), the \(z\) - value is \(1.28\) (from the symmetry of the standard normal distribution, \(z_{0.10}\) is positive).

Step2: Find the corresponding values for \(z_{0.05}\)

For a right - tail area of \(0.05\), looking at the standard normal table, the \(z\) - value is \(1.64\) (since the area to the left of \(z\) is \(1 - 0.05=0.95\), and from the standard normal table, the \(z\) - value corresponding to an area of \(0.95\) is \(1.64\)).

Step3: Find the corresponding values for \(z_{0.025}\)

For a right - tail area of \(0.025\), the area to the left of \(z\) is \(1 - 0.025 = 0.975\). From the standard normal table, the \(z\) - value is \(1.96\).

Step4: Find the corresponding values for \(z_{0.01}\)

For a right - tail area of \(0.01\), the area to the left of \(z\) is \(1-0.01 = 0.99\). From the standard normal table, the \(z\) - value is \(2.33\).

Step5: Find the corresponding values for \(z_{0.005}\)

For a right - tail area of \(0.005\), the area to the left of \(z\) is \(1 - 0.005=0.995\). From the standard normal table, the \(z\) - value is \(2.58\).

Answer:

\(z_{0.10}=1.28\), \(z_{0.05}=1.64\), \(z_{0.025}=1.96\), \(z_{0.01}=2.33\), \(z_{0.005}=2.58\)