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Question 6 (1 point) Mr. Britten recorded the grades his students scored on a math test. He wants to make a dot plot to represent the data_ How manymore dots will b...

Question

Question 6 (1 point) Mr. Britten recorded the grades his students scored on a math test. He wants to make a dot plot to represent the data_ How manymore dots will be place above the 100 than above the 70,75,and 80 combined?Grade Scored on Test 100 85 90 95 85 95 100 80 100 90 70 100 75 95 100 75 90 100 85 95

Question 6 (1 point) Mr. Britten recorded the grades his students scored on a math test. He wants to make a dot plot to represent the data_ How manymore dots will be place above the 100 than above the 70,75,and 80 combined? Grade Scored on Test 100 85 90 95 85 95 100 80 100 90 70 100 75 95 100 75 90 100 85 95



Answers

Solve each problem. See Examples 8 and 9. Greg Tobin scored 92 and 96 on his first two tests in "Methods in Teaching Mathematics." What score must he make on his third test to keep an average of 90 or greater?

So now we have the full of versatile Tim. 94 plus 86 plus 84 last 90 several and ah found five. The thieves exam. We assume that s ass X average Sony Teoh derided by five. And then we need it. You larger than where you chose to 90 So we can street can modifiable side by five. And then we have 94 plus every six last 84 Class 97 that he goes to a 361 Last access larger than recalls to for 100 and 30. So ax here as Eco's too 81 So caused the Maximo s Hendry so last in my Hendry So he needs at less 89 for the

The instructor announced to his class that the recent exam scores were bell shaped so we can draw our bell shape and as soon as we hear that bell shape, we should be thinking empirical rule and the empirical rule says that in the center of the bell shape will be your mean And within one standard deviation of the mean. So that would be one standard deviation to the right and to the left. It will account for approximately 68% of the data. Within two standard deviations of the mean, so that would be to above or two below. That will account for 95% of the data, and within three standard deviations of the mean Will be approximately 99 7% of the data. Now, since the bell shaped curve is symmetric, then On each side of the mean will be congruent parts, mirror image, but congruent parts, so therefore the 68% can be divvied up into 34% to the left and 34% to the right. Or as a proportion That would be .34 And between two standard deviations away, there are four parts. Two of those parts are already defined to account for 68%. So that means there's 27% left over to be split, evenly making the section between two standard deviations Below the mean and one standard deviation below the mean to be 13,5 And the other part to be 135%. And as a proportion that would be .135. Since the 99.7% section is broken into six parts and four of them are already defined. They total up to 95%,, Meaning there is four 7% left to be split evenly. So that would make 2.35% in each section And as a decimal that would be .0235. So let's use this information to solve the problem that we have. So on this particular test we had a mean of 75 And a standard deviation of five. So we're going to draw our bell curve With that information so we're gonna play 75 in the center. We're going to Add a standard deviation will be at 80. If we added two standard deviations, we'd be at 85 And if we add three standard deviations we would be at 90 on the other side. If we subtract A standard deviation will be at 70. Subtract two. Standard deviations And subtract three standard deviations. So now we can also put in our proportions This would be 3, 4 and 34 Accounting for 68% of the data. This would be .135 And .135 accounting for mhm 95% of the data. And we'd have .0235 in each of these and three standard deviations away from the mean Would account for 99 7% of our data. So now we're ready to answer our questions in part A it's asking you what is the median of this data? Well, in a bell shaped curve, the mean, the median and the mod are all equal, And we were already told that the mean was 75, Therefore the median would have to be 75. In part B, we need to approximate How many students are, what proportion of students scored between a 70 and an 80. So if we look at our custom bell shaped curve between a 70 and an 80 would be 68% of the data Or as a proportion that would be 68 for part C. I recommend drawing the curve again. So we are trying to determine what proportion of students scored above 85. So if we draw that curve again He had 75 in the center and then we had 80 85 90 and 70 65 and 60. Then above an 80 you're sorry above an 85 Would account for these two parts And we know that between the 85 and the 90 was .0235 but we don't know the part above the 90. So the easiest approach to this is to start with the fact that A whole curve would be one. If we take away half the curve We're taking away five. Then if we take away the section between 75 and 80 then we are removing 0.34. And if we take away the section between the 80 and the 85 we are removing the .135. Therefore the proportion above an 85 is going to be point 0 to 5 or 2.5%. And then part D. What is the percentile rank Of an 85? So again I recommend drawing our picture, make it work for you, make it interactive. So when you're talking percentile rank, percentile means how many scored below you. So if you're scoring at the 30th percentile, that meant 30% did worse and 70% did better. So we need to know what percent did worse than an 85. So we're trying to figure out what percentile or what percent of the curve would be shaded. So from here on back is 50% in between 75 and 80 was 34 And between 80 and 85 was 13.5%. So when we add those parts together, 50% plus 34 Plus 13.5%. We find that 97 5% of the students scored lower than an 85. Therefore, the percentile rank of an 85 is the 95, sorry, 97.5 percentile.

See that the average from the midterm and final must be between 79 19 inch again. Don't be so. It means that the average baby between 79 in 19 inclusive means standing in for him as well. And they are rich on the midterm and final means that we have the midterm press. The final, even with Julia's average, must be different. 79 on the 90 we know the midterm is 65 really plus the final chill 79 yourself for the final great hand we need. You want everything to beat you, beat you By being done we see that you can sing with Children who have only 65 final end of media And now on it your imprints We gonna 79 I'm still go to 150 ain't And on him we're gonna 180 on. Then we were searching the 65 from it. Up them get included. You minus 65 this under 93 0 fi. No way between wanting the minus 65 it would be more than a tiresome is done. We'll be eyes a hand right here on then That would be the ranch for the fun of great needed to get Toby for lucky

In this problem we have to construct the dot plot for the for AIDS and schools in an introductory statistics squares. Oh okay. Yeah. Mhm. So first we'll draw horizontal axis. So here's your horizontal axis that displaced possible values of the quantity to NATO. Okay. So if you see the minimum value here is 34, maximum Around 100. So we'll plot From 30 200 So we'll start with 13. Mhm. Soon Here if you see to be 35 and This will be 14. Yeah This move a 14. Yeah. Just give me 45 mm 15. Okay let's keep five. Mhm mm 16. The music's too quiet. Mhm. It's moving 17 feeling It is 175 80 185 in 19 95 And it's going to be a 100 sooner. It's my first observation. Just we have to record each observation by placing a lot over the appropriate value on your glasses. So if you see 88 it is over here. Yeah. Mhm. I'm 82. Yeah, 89. Uh huh. Yeah. Okay. Mhm. Yeah. Is 85- 88. Okay. Is over here and take it to it's going to be here mm. From 89 Next to 88. No. Mm hmm, 17. Mhm. All right, 85. Pretty Girl. Great, 63. Yeah. Thank you. 100. Cool. Yeah. Mhm. 86. Mhm. Okay, 67. Okay. Mhm. 39. Mhm. Mhm. 19 96. Mhm. Mhm. Mhm. Oh, Mhm. 76. Yeah. Okay. 34. What? 81 64. So my In full in 83 and 64. Let's do. Mhm. Stupid thing. 75. Yeah. Yeah, 84. Right. Mhm. Mhm. 89. Okay. Yeah. So we can mark a baldy Bolivia is blocked, you know, Because it's again you can talk about it, mm hmm. Yeah. Yeah. Please don't. Mhm. You see this is uh Mhm. Dark locked. Mhm. Yeah. What


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