Question

find the critical value ( z_{c} ) necessary to form a confidence interval at the level of confidence shown below.
( c = 0.86 )
( \begin{aligned} \frac { 1 } { 2 } ( 1 - c ) & = \frac { 1 } { 2 } ( 1 - 0.86 ) \\ & = 0.07 end{aligned} )
while you can use a standard normal table or technology to find the critical value, for this problem we will use
a standard normal table.
use a standard normal table to find the positive critical value that corresponds to a tail area of 0.07.
( z _ { c } approx ) (round to two decimal places as needed.)

Explanation:

Step1: Calculate the tail area

We have already found that the tail area is \(0.07\).

Step2: Use the standard - normal table

Looking up the value in the standard - normal table (the \(z\) - table), we find the \(z\) - score corresponding to an area of \(1 - 0.07=0.93\) (since the standard - normal table gives the cumulative area from the left).
From the standard - normal table, the \(z\) - score corresponding to an area of \(0.93\) is approximately \(z_{c}\approx1.48\)

Answer:

\(1.48\)