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Please solve using appendix table and show steps(9) Let Z be a continuous random variable with Z∽N(0,1) . Findthe value of the following. 1.(3) z0.025 2.(3) z...

Question

Please solve using appendix table and show steps(9) Let Z be a continuous random variable with Z∽N(0,1) . Findthe value of the following. 1.(3) z0.025 2.(3) z0.90 3.(3)η(0.1), the 30th percentile of standard normal distribution.

please solve using appendix table and show steps (9) Let Z be a continuous random variable with Z∽N(0,1) . Find the value of the following. 1.(3) z0.025 2.(3) z0.90 3.(3) η(0.1), the 30th percentile of standard normal distribution.



Answers

Find the indicated z-score. Be sure to draw a standard normal curve that depicts the solution. Find $z$ -scores that separate the middle $99 \%$ of the distribution from the area in the tails of the standard normal distribution.

This is my standard normal cough where my immune or my center is zero. And my sigma standard deviation is one. So I mean a zero and a standard deviation is one. Now I want to find the Z schools that separate the middle. 94%. Right? Let's say that these are my Z scores. This will be minus here and this will be easy. Okay, that's a present middle. 94% of the distribution from the area and the tales of the standard normal distribution, Which means this entire area has to be 94% or 0.94 which means that the area in these tales has to be 0.6 Since it is symmetric, the area in one of the tales has to be 0.3 So what I'm using is a critical value calculator. I put in my l 50.3 and I get my critical value is 1.88 So this is 1.88 So since the symmetry, this will be minus 1.88 and these are the scores that I want

So we'll start by drawing a picture for a The key to solving A is realizing what the 33rd percentile actually means. And what that means is that there's a value 33rd percentile such that 33% of the values fall below that value. So in other words, 33% of the area is to the left of the sudden score that we're looking for. So the red area here is equal to 0.33 And to find the sudden score, we're going to use our standard normal table and we're going to look for an area that corresponds with 0.33 So we'll go over to our table. We start at the top. We see that these values are all way too small. So we keep scrolling down and we look for Sarah 0.33 So the closest values to 0.33 are given here and we see that the one on the left course ones with a set score of negative zero point for three on the one on the right, corresponds with his outscore of negative 0.44 So we're somewhere between negative 0.43 and negative 0.44 And so a natural guest would be negative 0.3 five for a for be. You want the middle 40% of the area. So this red area here is going to be equal to 0.4, which tells us that the area in the tales is going to be equal. Teoh which value? Well, we know that the total area needs to sum up to one. So the leftover area, if we take away 0.4 is gonna be Sarah 0.6, and then we divide that into those two tails, and we're gonna get Sarah 20.3 on either side. So now we want to find the twos at scores that correspond with founding this middle 40%. So to do that, we're gonna find his head score on our table That corresponds with an area to the left of it being equal to 0.3. So on our table, we're gonna look for a 0.3. It should be fairly close to what we had here. So it looks like it's gonna be somewhere between here in here. So the one on the left corresponds with this. That score of negative 0.5 to and the one on the right course ones with that score of negative 0.53 So we're somewhere between these two values and the natural gas would be negative 0.25 for these that score on the left here. But this that's forming the right. We're going to use the fact that the normal distribution is symmetric, and so the that's going on, the right is going to be the positive version of this. That's where on the left, so it's just going to be sterile. 0.5 to 5.

In this question, we want to find a sheeted area under the standard normal distribution curve. We want to find the probability in which a sample Z is between 1.23 and 1.90 We can calculate this value using a graphic calculator. Since digital standard normal distribution, we set the mean to zero and standard deviation toe one. As for the other parameters, we should set the upper bound to 1.90 and the lower bound 1.23 The answer is 0.806


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