Determining the Critical Z Value | Calculation and Explanation

Find the indicated critical Z valuefind the value of -za/2 that corresponds to the confidence level of 89.48%

To find the critical Z value, we need to use the Z table

To find the critical Z value, we need to use the Z table. In this case, we are looking for the value of -za/2 that corresponds to a confidence level of 89.48%.

First, we need to determine the area to the left of the critical value in order to find the corresponding Z value. Since we want to find the critical value that corresponds to a confidence level of 89.48%, we need to find the middle area.

Since the total area under the normal distribution curve is 100%, we subtract the confidence level from 100% to find the middle area:
100% – 89.48% = 10.52%

Since this is a two-tailed test, we divide the middle area by 2 to find the area in each tail:
10.52% / 2 = 5.26%

Now, we can use the Z table to find the Z value that corresponds to an area of 5.26%. The Z table provides the area to the left of the Z value.

Looking up the closest area to 5.26% in the Z table, we find that it corresponds to a Z value of approximately -1.645.

Therefore, the indicated critical Z value or -za/2 that corresponds to the confidence level of 89.48% is approximately -1.645.

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