Need help finding the critical value

Question

Find the critical value z of 83%. Round to two decimal places.

I get it all divided out but when it comes to finding the critical value I have no idea how to find that number.

Answer 1

The critical Z is simply the z value associated with the cumulative probability the problem requires. You might be asked to find the Z score associated with p(Z < z) = .83, p(Z > z) = .83, or the z values lying between -Z and Z covering 83% of the distribution, i.e., an 83% confidence interval

I'm going to assume that you're looking for an 83-percent confidence interval. To find the -Z and Z at the edges of this interval, do the following:

1.) The area of the normal distribution NOT included in your 83-percent confidence interval is 100 percent - 83 percent = 17 percent.

2.) Split the 17 percent into half, one for the upper tail and one for the lower tail of the Z distribution. 17/2 = 8.5 percent.

3.) So, you will want to find the Z score for p(Z <= z) = .915 and the Z score for p(Z<= z) = .085. You can use the NORM.S.INV function in excel or any Z-table to look up these values. You'll only need to look up one of the Z scores. Because the confidence interval is symmetric, the other Z score will be (-1)* the one you looked up., e.g., NORM.S.INV(.085, TRUE) gives a Z score of -1.372. The Z score for p(Z <= z) = .915 is then 1.372