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DistribuStandard Normal Table (Page 2)ofthe Standard Normal Table (Page 2) placesPOSITIVE z Scores Standard Norma Distribution: Cumulativo Arca from the LEET5000 53...

Question

DistribuStandard Normal Table (Page 2)ofthe Standard Normal Table (Page 2) placesPOSITIVE z Scores Standard Norma Distribution: Cumulativo Arca from the LEET5000 5396 57ar50+6 54585080 54786o70 5676 6o26G5C559650486062 64446255 6628 6,985 7374Gce4#0uCHnG6540766Gtom 704ERX489so7757 75604540Eno8024B070a508a64E 0449 9032A7um 4907 040?9049 9107 93459ogi97r94060559597Done

distribu Standard Normal Table (Page 2) ofthe Standard Normal Table (Page 2) places POSITIVE z Scores Standard Norma Distribution: Cumulativo Arca from the LEET 5000 5396 57ar 50+6 5458 5080 5478 6o70 5676 6o26 G5C 5596 5048 6062 6444 6255 6628 6,985 7374 Gce 4#0u CHn G654 0766 Gtom 704 ERX4 89so 7757 7560 4540 Eno 8024 B070 a508 a64E 0449 9032 A7um 4907 040? 9049 9107 9345 9ogi 97r 9406 055 9597 Done



Answers

Find the $z$-score for the standard normal distribution shown in each of the following diagrams.

The key to solving these problems is remembering that the total area under the curve is equal to what? For a We know that the areas of the left of the set score is 0.7673 So we're going to use our standard normal table and look for this value. We're looking for the closest value to 7673 and we see that this value is directly on our table and it corresponds with us. That's where a 0.73 for be. We have the area to the right people to 0.7190 And since our standard normal table only gives us the area to the left of that, scores were going to calculate the area to the left, so this is gonna be equal to one minus 0.7190 And when we typed that into our calculator, we get 0.281 So now we're gonna look for that the 0.281 on our standard normal table. So you see that this value here is very, very close to what we're looking for. And if we were to round it than this value will be equal. And this corresponds with the set score of negative 0.5 eight. So it's approximately negative 0.58 And if you wanted, you could get more a bit more specific with that by finding the two closest values and then inter plating between those values. And first, see, we're gonna be looking on our normal table for while you quit 151 size. So that's gonna be a a little bit higher up this time. So here we have 0.15151 And again, if we were to round this, this would be equal to the value that were being asked about. So we've got negative 1.0 three as that's that's for. So it's approximately negative. Well, my 03 and again, to get a more precise answer, you could find the two closest values on the table and then interplay between those values

All right. And this problem we wish to use a normal distribution to be able to find the following the scores. A through D. This question is challenging understanding of how to match the score in a normal distribution to the associated area under the curve. To solve its first review relevant material for normal distributions before proceeding so as detail remember that's the scores on the probabilities. So an example the probably the greater than zero equals peanut implies that the area and purple peanut is the area to the right of arsenal scored. As an example, the probabilities is greater than 0.5 because the area on either side of these normal distribution is equal symmetric or one half. To solve this problem, we need to rely on two properties normal curves. First, the symmetry of the normal curve as well as the fact that the total area under the normal curve is one. So with this logic, we only need to solve proceeding through we see that A through D all can make use of symmetry us all. So first for part A we can write this as quickly as the probability less than that gives, you know, is one minus 10.95. Over to that is this 0.25. Area each Tales the corresponding Xena plus or minus 1.96. We apply the exact same principle to solve B through D. So it be the probability of the tail is one minus point number two equals 20.5 giving zero equals plus or minus 2.33 and see the area in the tales 0.170 is plus or minus 0.96 and finally, indie the area, and the tails is 0.135, giving zero plus or minus 3.0.

Uh huh. In this problem we wish to use the normal distribution table to find the following Z scores given for a through this problem is challenging our understanding of how to understand the relationship between the Z score in the area under a normal curve or C under normal distribution to solve. Before we proceed to find these Z scores directly, we're going to relate or rather review relative information for normal distributions. So as the people have the scores on the probabilities as we weren't as an example that probably these great additions and you know it's peanut or peanut is the area in purple and not as much as black as an example is the standard normal distribution has a mean zero, probably these great and 0.5 or half the area under the normal. So to solve this problem we need to remember the symmetry of the normal case. That is probably the lessons do not is probably greater than negative Z not similarly, we have to remember that the total area is one. Well, this is the reason we only need to solve so the probability lessons, you know, equals 0.9 gives. It probably is is less than negative United's 0.1. Thus Z 91.28 probably easy lessons, you know, it's .5 is equivalent to the is he not equal zero. This is from the identity we identified above coincidentally see probably the greater than zero equals 00.1 is probably the lessons are not equal 0.9 this time again, Xena is 1.28 because A and E are equivalent Fergie. The probably the greater than 0.9 is now negative 1.28 by symmetry. Finally, and I've heard either probably easy Between negative 1.24 and 19.8 is probably the lessons do not mind is probably less than negative 1.2, So I went to the scene gives 1.33.

All right. And this problem we wish to use a normal distribution to be able to find the following the scores. A through D. This question is challenging understanding of how to match the score in a normal distribution to the associated area under the curve. To solve its first review relevant material for normal distributions before proceeding so as detail remember that's the scores on the probabilities. So an example the probably the greater than zero equals peanut implies that the area and purple peanut is the area to the right of arsenal scored. As an example, the probabilities is greater than 0.5 because the area on either side of these normal distribution is equal symmetric or one half. To solve this problem, we need to rely on two properties normal curves. First, the symmetry of the normal curve as well as the fact that the total area under the normal curve is one. So with this logic, we only need to solve proceeding through we see that A through D all can make use of symmetry us all. So first for part A we can write this as quickly as the probability less than that gives, you know, is one minus 10.95. Over to that is this 0.25. Area each Tales the corresponding Xena plus or minus 1.96. We apply the exact same principle to solve B through D. So it be the probability of the tail is one minus point number two equals 20.5 giving zero equals plus or minus 2.33 and see the area in the tales 0.170 is plus or minus 0.96 and finally, indie the area, and the tails is 0.135, giving zero plus or minus 3.0.


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