 Hi Brandon and folks Brandon brought up this question that he saw on the midterm for which he hadn't Seen an exact example and just paraphrasing the exam from Brandon says Find the Z scores for which 80% of the distribution areas lies between minus Z and plus Z Brandon shows you a good example of how to do that using Excel I thought I would show you how to do it using stat crunch as well So, you know, those of you who are using stat crunch can see it. Let me bring up stat crunch and As Brandon said, let me bring the problem down again as Brandon said The key to this is to think about what it's really telling you. It says 80% is between minus Z and plus Z and since the normal standard normal curve is Symmetrical if 80% is between minus Z and plus Z that means 10% is to the left of minus Z and 10% of the area is to the right of plus Z so we need to find the Z's for which the Probability and if you remember on the normal curve, you know when we saw for a Z We're given the area under the curve or the probability From negative infinity up to that value So we can think of it that way. Let's look at stat crunch I'm going to go to stat and again what I did here. I went because I'm not in my stat lab I went to statcrunch.com all of you that have access to my stat lab can get into stat crunch Using your my stat lab credentials, but we just go to stat calculators Normal calculator and we bring up our good old standard normal curve and Because we are using Z values We just leave the standard the standard normal values of the mean of zero and a standard deviation deviation of one Let's solve for the minus Z the lower side first so we leave our less than or equal pointing to the left the lower side and we have 10% of the area there that means just by clicking on compute the Minus Z is minus 1.282 rounding the three decimal places and again Don't worry if stat crunch or excel gives you a slightly different answer than my stat lab. I will check all the quizzes and exams and generally I find these places and give you credit if you're Round off is is the reason that you don't have the the answer. So that's the lower side the the minus Z and by inspection you you know We know the normal curve is symmetrical. That means the plus Z would be plus 1.282 But let's just check and see I want to click on the greater than symbol to get us into the right half of the curve and Let's put our point one in again for the 10% that we want for the upper end and Click on compute and we can see that this 10% area above Z gives us again a Z of 1.281 Did I do that right? Yeah, that that's the same value So that that's a quick way to do it with with stat crunch and really you can do it with any values if they gave you you know 30% on the low side and 10% on the upper side Just put those values in stat crunch and click compute. So I hope this helps