Critical Values. In Exercises 41–44, find the indicated critic...

Question

Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.

z0.90

Accepted Answer

Hello. In this video, we are going to be finding the critical value of Z 0.85. So the problem here says that we want to assume that the heights of a group of students are normally distributed. We want to find the critical value of Z 0.85 and round the result to two decimal places. So, let's just go ahead and draw an image. First, we know that we are working with a normally distributed. Amount of data So, we are going to draw a normal distribution, which follows a bell-shaped curve, and this bell shape is going to be centered at 0. Now, what we want to do is you want to find the critical value of Z 0.85. Now, what this is saying is that we want the probability of Z behind some number X, and the output of this probability is going to be 85% or 0.85. We don't know exactly where that lies on the normal distribution. So, but what this would look like is if we had a cut off here. Now, at this cutoff, we don't know the critical point, so we're going to label that as X, but what we do know that the entire area to the left of this critical point is going to have a total of 85%. So what we need to do is we need to identify the value on the Z table. That has the value 0.85 or is as close to 0.85 as possible. And what we are looking for is the values to the left, which are the critical points of the Z table. Now, in this case here, if we read the Z table, we are going to get the value of X equal to 1.04. This is going to be the critical value that has a normal distribution or a probability of 85% to the left of it. And with that being said, the solution to this problem is going to be B. So, I hope this video helps you in understanding on how to approach this problem, and I will go ahead and see you all in the next video.

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Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.

z0.90

Key Concepts

Critical Value

Z-Score

Standard Normal Distribution

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Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.z0.90