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8 (Type 5 1 (Jsipe 2 3 03 Using the select vour ioteger (6leger 99 d) Aboul what percent 1 1 Integers or Imienid what percenl of people : 8 Ji 1 answer deleirb deci...

Question

8 (Type 5 1 (Jsipe 2 3 03 Using the select vour ioteger (6leger 99 d) Aboul what percent 1 1 Integers or Imienid what percenl of people : 8 Ji 1 answer deleirb decimia of people le about inoqe of people 2 JU EXHCCL should have should have rouneople rouncople rouneople 0 [i [i of tho IQ scoros 1 3 1 1 have above scores I0 scores scores belwgen 1 and 1 1 602 AVOYE found? andChoose 1 mode test is 1 standardized I0 scores that conectly 1 1 anal { 3 pue standan predicts viation 1 0f 20 Scom(}

8 (Type 5 1 (Jsipe 2 3 03 Using the select vour ioteger (6leger 99 d) Aboul what percent 1 1 Integers or Imienid what percenl of people : 8 Ji 1 answer deleirb decimia of people le about inoqe of people 2 JU EXHCCL should have should have rouneople rouncople rouneople 0 [i [i of tho IQ scoros 1 3 1 1 have above scores I0 scores scores belwgen 1 and 1 1 602 AVOYE found? and Choose 1 mode test is 1 standardized I0 scores that conectly 1 1 anal { 3 pue standan predicts viation 1 0f 20 Scom ( }



Answers

The following list of test scores has an average of 50 and an $S D$ of $10 :$
$\begin{array}{lllllllllll}{39} & {41} & {47} & {58} & {65} & {37} & {37} & {49} & {56} & {59} & {62} & {36} & {48} \\ {52} & {64} & {29} & {44} & {47} & {49} & {52} & {53} & {54} & {72} & {50} & {50}\end{array}$
$\begin{array}{l}{\text { (a) Use the normal approximation to estimate the number of scores within }} \\ {1.25 \text { SDs of the average. }} \\ {\text { (b) How many scores really were within } 1.25 \text { SDs of the average? }}\end{array}$

Okay, So the question here is so given a normal distribution of test scores, um, the mean is 50. And the standard deviation is it, um, so are mean is 50 and our standard deviation is equal to eight. Um, given, like, what is ours? E score. We want to find the Z score. Ah, of 38 in this normal distribution. Um, okay, so the formula for disease score is just take our value. 38 subtract the mean, which in this case is 50 and divided by the standard deviation. So this I'm actually tells us how many standard deviations above or below the mean are set of our, um, unit of data is so in this case, 38 minus 50 is negative. 12 divided by a. And we get negative three over two, which is equal to negative one and 1/2. Um, so that is our Z score. Um, and referring back to the problem that is answer choice number two. So that is your answer. Z score is negative. 1.5. Meaning it's 11.5 standard deviations below the mean, and that is choice number two

For this question, we're told that scores for an exam are normally distributed and have a mean score of 525 and a standard deviation of 80. For Part A were asked what percentage of of testers score less than 350 on the exam. We're looking for the probability that X is less than 350 and to convert his head scores were using that is equal to X minus mu over Sigma. So this is equal to the probability that said is less than 350 minus 525 over 80 just equal to the probability that said it is less than minus 2.188 equals 0.144 So the probability of scoring less than 350 is 0.1 for four or, in other words, 0.144 of the students to take this exam score less than 350 for Part B, whereas what score is needed to make the top 12%. So we're looking for a score K, such that scoring higher than it is equal to 12% or a 0.12 probability of scoring higher than K is equal to 0.12 Another way to state this is to say the probability of Zed being less than K minus 525 over 80 is equal to 0.12 So you can look in the standard normal table or use a calculator or software to find the said value that has a cumulative area of 0.12 And that gives us value a zed score of 1.175 So we can say that K minus 525 over 80 is equal to 1.175 and therefore K is equal to 619 So you must score higher than 619 in order to be in the top. 12% of testers report see, were asked what the inter quartile range is. So the inter courthouse range is the range from the first quartile to the third, so the range is the difference of these court tiles. I remember the probability that of scoring less than the first quartile is equal to 0.25 So we can say that the probability of Zed being less than Q one minus 525 over 80 is equity 0.25 So we have Q one minus 525 over 80 is equal to 1.175 So this 1.175 is this ed score that has a cumulative area of 0.25 So therefore, yes is equal to you. This which were showing in this equation here. So then isolating Q one we get Q one is equal to 471 0.8 and then we can do the same thing for the beard quartile. But the probability that said is less than here three minus 525 over 80 is equal to 0.75 which tells us that Q three minus 525 over 80 is equal to zero point 67 four and then isolating que gives us 578 0.92 So those were the bounds on our intercourse. How range so to find the size of the range, we just subtract those two values where we subtract Q one from Q three and we get 107 0.84 So this is the answer now for Part D. Were asked, What grade do you need so that only one out of 500 score above it? The one out of 500 is equal to 0.2 So we want to find the probability of scoring greater than a value K being only equal to 0.2 So what value of K such that the probability of scoring higher than K is equal to 0.2 So we can say the probability of Zed being less than K minus 525 over 80 is equal to 0.2 This should be three zeros in here. Well, sorry. No, it's it's 200.0 to Okay, we're good to go. So we can say that K minus 525 over 80 is equal to you. 2.878 And that gives us K is equal to you. 755.2. So you must score higher than 755.2, such that only one out of 500 score that high

For this case a normal distribution is assumed and new and sigma given in the problem for the I. Q. Is 115. But if you now it is asking the mobility between the Values 1900 and 10, So 90 will be on left side, 110 will be on the right side. Yeah. Is that for 19? It will be Yeah. A couple of years. Thank you. 19 minus 100 by 15 which is -2 lately. Is that 4110 is? Yeah. Mhm. To my tree, I don't know anything. So because inside area will be Mhm. Yeah. This quantity which can also be written as P Yeah minus He's at less than -2. Mhm. This value from the calculator or at that table can be calculated as so you can find it from the table and the final answer here will be 0.4972.

So the following question is of normal distribution Plot. So this is the kind of normal distribution. This maximum is the meaning valley which is mean 1st 200. The sigma sigma is 16. So This is a 100 The 16 and this value will be minus 84. This will be sigma and this also will be signal. So this area is known as that value. Well the percentages area is determined by Yeah. Mhm Mining by Zaydi schools. Yeah. So for the this is the plot. This is the solution of part. Mhm Yeah. No. Does that export that is given us X minus X. Bar for example 04. Yeah this case 116 minus 100 upon sigma. So that because it will be one. So for this yes The area is for that equals to one. Yeah The probability percentage is 68% nearly. And this value are derived from that table. Mhm. So we'll finally see the values from that table. The middle area Since 20% is us exactly will always be causes that you have to see this middle area. Not not this area. So this many other people are in this form so you will get the wrong answer this is that correct correct Zach devil From this. We have derived for the cost 180-68% for the value 99.7% concept able we have derived the value of state and for the value 95%. The value is approximately close to Yeah. Is that when you will be close to nearly equals two. But these are the answers for the part third part C part It is asking yeah What interval would you expect the 95% of Yeah sorry be part it is asking in what interval you should expect the 95% of I. Q. Schools. So for that interval to Yeah two Which means 95% which is we were in the question he calls to 95% interval will be that's minimum will this this X men two X max It is asking, strikes minimum will be expand minus two times of sigma. X maximum will be X one plus of two times of sigma. This is basically derived from here only. So it will be 100 -3-16. Yeah that is nearly 68 100 plus two into 16. It is nearly 1 23. So this is the interval from 60 years, 68- 1 30. All right, this is the part to be look the part C says what values will like above this value. 1 16. So we know that 1 16 this is up to sigma we have seen earlier. So he is greater than one asking basically it is asking for this case. This area should be returned my this is my formula He is that close to one range I want to 20 that equals to an area inside area Here's 68%, -68 x two which is Nearly equal to 16% of talks. This too why we did these tubes? Because after reducing this area we will remain the this both area will remain so we have two divided by two to get only this area Only one side is required. Yeah. Yeah. The party is asking again, I hope you have understand the method Interval 68-84 in Durban 68 84. So this much of area is asking it is Z equals 2 -2, this is that equals -1. So he uh for was to be Is that equals 2 -2-? Is that equals 2 -1. So this much area is required So is that equals 2 -2 will be simply by mhm total my upon half which we can say mhm It is a value 95.4 to 95.4.2 This will lose nearly 67.8% 67.8 by it. So we can simply subtract .6 seven I want to which is mhm 13 point yeah, What you need is 13.8 in the last part It is asking for Values greater than one today. 1:30-1:30-100 Sigma 16. So this is basically to signal the last part is also very easy. He said later than two. It is asking which will leave one might not be adequate. It was, it was -21 Which is nearly 1 -25.4 percent. Like to one or we can say hundreds 100%. Yeah, So it will be nearly equals two. Yes, 4.652, which is nearly constitute 20%. So since half is where we will, but I hope you understand this concept.


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