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Number of classes: 8 Data set: Finishing times (in seconds) of 20 male participants in a SK race1719 1447 1960 18191630 1251 1525 20201573 1801 1824 20811471 1598 1...

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Number of classes: 8 Data set: Finishing times (in seconds) of 20 male participants in a SK race1719 1447 1960 18191630 1251 1525 20201573 1801 1824 20811471 1598 1618 15802297 1779 1304 1480

Number of classes: 8 Data set: Finishing times (in seconds) of 20 male participants in a SK race 1719 1447 1960 1819 1630 1251 1525 2020 1573 1801 1824 2081 1471 1598 1618 1580 2297 1779 1304 1480



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Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns. Number of classes: 8 Data set: Finishing times (in seconds) of all male participants ages 25 to 29 in a $5 \mathrm{K}$ race $$\begin{aligned} &\begin{array}{llllll}1595 & 1472 & 1820 & 1580 & 1804 & 1635 \\1959 & 2020 & 1480 & 1250 & 2083 & 1522 \\1306 & 1572 & 1778 & 2296 & 1445 & 1716\end{array}\\&1618 \quad 1824\end{aligned}$$

And this question we're told that the average finishing times among high school boys in a track event is five minutes and 17 seconds five minutes 17 seconds, that's the average, which is basically 317 seconds and the standard deviation is 12 seconds. And we're told that the qualifying time is to be said that only the fastest 5% qualify. So this is the normal distribution we want and this is our mean we want the fastest 5% so we actually want those who are who have the shortest times, so we want the fastest 5% here. So the area here is point of five, and the value here is X. Star were asked to find the qualifying time Ex Star. So we start with our standard normal random variable quality easy, less than the star is 0.45 And from there we basically get our value of C. Start to b minus 1.645 from our table. And the qualifying value of the time, ex star is basically the start times. The standard deviation plus are mean which gives us 297.26 seconds or 4.95 minutes. That's our answer to part A. In part B. We're told that in the Western region the boys are normally distributed with standard deviation 12, the same standard division, but higher mean of 322 seconds. We're asked to find the proportion who qualified to run in this event. So the proportion that qualified to run is the basically those who have a faster time than the qualifying times, the probability that access less than 297.26 seconds, converting that to our Z value, which you call it easy, less than minus two, Final six. And probably to hear 0.197 star proportion is approximately 1.97 or 2% who qualify from the Western region.

So in this question were given data about 800 m freestyle event. So the meantime in this event waas 502 point 84 seconds standard deviation 4.68 seconds and were asked to apply Shall be chef serum using K is he hopes to. So here she bishops theory, um, basically states that the percentage off data that lies within K standard deviations is he goes toe one minus one over K squared times 100%. So the percentage of data that's going to lie within two standard deviations in this case is one minus 1/2 squared times 100% which is 75% off. The data is going to lie within two standard deviations. So if we look at our data, you have the mean and standard deviation. So we're going to take two standard deviations above the mean in two standard deviations below the mean So our values for that are so we're going to say 75% off. The data lies between so two standard deviations above the mean is basically two times 4.68 plus 5 2.84 which gives US 512.2 seconds on the top and on the bottom, we have two times 4.68 and five, or 2.8 for minus that, which gives US 493 0.58 So, according to Chevy Chef Serum, when case equals 2 to 75% off, the data lies between 493.58 and 512.2 seconds.

In this problem Off frequent participation we have to construct the frequently distributional tables on the big music is too damp. So they're given Create a set. The number of class is this h So you have a number of classes given his age, sort of the sample sizes. But the other thing you this. So now we reversed Find the class, but using the formula bench to buy the timing growth analysis. So you are the dangers. 514. No minimum valueless. 291 500 14, minus 2 91. Divided by 820 Both job 2023 by eight Just approximately three. Music company Convenient Operalia You. This would be because 514 No restaurant in Tirana divide about eight will give us 27.8, which is we came down with Stoop. The next Dominion value was 28. It's just acquainted approximately for between three. D. Actually, she knowledge we constructed Diego. It was there. It's what e Uh huh. Yeah, it's That's okay. So first, let's do the class. Okay, So tell limit starts with to 91 people. Okay. Oh, in the class with his 20th since the class. Not all that. We just had 27 2 words. So up to 91. Class 27th to where? Yeah, it's That was 318. 10 minutes. 2300 and 19. 48 in the last 27. It's 3. 46 would be four peaks. Seven going to be 74 make. Okay. Yeah. What? Please. 75 before not going. 403 two fold. Lefty, it sold 31. Okay, but 24 58. So 59 24 86. We found 87. Just 500 from pain. So this gives us eight classes to the number of classes. Syndicated number of class family. Find the pregnancy happen. Frequency give. So we're 91 for 3, 18 years. One doing this. The screen dollars. It's it was That makes sense. Thanks. Difference. Yeah. Find it's helping them. And e. Right and frequency 4, 319. 346. It's one. Keep doing it. Green. It's okay. But before 3. 40 73 74. Yes. Once get Hmm. Thank you. And train? Yeah. No. 3. 75 to thrown off group. It's one. Children, please. She four five. So not three, 24 13. 12 Name sold. Five. Yeah, it. Yeah, thanks. It's it sucks for 31 to 4. 58. Okay, it is company fun to to mean sword 4 59 to 4. 86. Okay, one Chester Bonomy for 87 to 514. You just tell just one. I'm too young. So this is a mission f this sample size, we calculate we can cross. Verify this. Yes. 30. Now we have to calculate the midpoint. That point will be no more glass limit. There's upper class limits divided by troops. That is, for the first class to 91 place, creating by tube, which was 2091 last 3. 18, not by which is 304 0.5. Next will be 319th. Last Yes, 3. 46 but guarded by just 332. My job. It's keep accepting. 332.5. We see the difference. The difference here is going to be 28. So we can just add 28. So the previous classes my point to get through. Yeah, my point of the current chaos. Just 360.5. 388. Well inside 306. But 416.5. It's 444.5. It mhm. 473.5. Yeah, 500.5. Okay, now we have to find out later. Frequency if. Yeah, just nothing. But but elective frequency frequent to the class frequency divided by sample size. Right now. Class frequency. Here it is. Five Bike 30 to week point 1667 Check. Take. Okay. When? Four by 30. But ah, 0.1333 Country by 13 you 0.1000 five by 30. Again, This one point point 1 67. It's six by 13. Thank you. 0.2 for over 30 years. Point once we leave one by 30 to the 0.33 I mean to buy. That is to the opponents of Europe. 667 50 c submission. If by end they're going toe one. But this some off. All the later frequency is going to be kind of job once. Now we have to calculate accumulated frequency so accumulated frequencies, Nothing but some off the frequency off that class and all the previous classes. So for the first class, that is five. The second classes problems five, which is nine. What justice? Biggest for this party to scrub or 93 here. It has been weak. 20 plus five inches. 17. What is 23? Somebody in plus six in 27 to make the deepest. 24 28 30. See, this is up. Sample sized. Now we have to constrict the frequency. His 2 g. I can't. Okay, so there is a frequency instagram. So the reaction times off 30 other females to end auditory stimulus. So if we see for the mid 0.304 point five, the frequency is five. Mhm. And the mid 0.3 are in 32.5. Frequency is Ford for 360.5. The frequency is three 288.5. Yes. Okay. It's so and mid point. 388. This five. And my point for 416. The six. It's so now we have to see the trend pattern off the saw. There does it. That is a instagram. So if we see the most of reaction times off between mhm, that is the midpoint. 416. Yeah. 3. 88 with 3. 75 to 4. 13 for 3. 74 to 4. 30. Okay. Thank you, particular. And recently just Missy. Mhm. Most of the reaction. Thanks. Would you like to says most of the reaction times? Okay. And between. It's 403 and 400 30 milliseconds. Yeah, it's What do you say? Because speech freedom, it's right.

Ready. So we're told that thes are Olympics winter sport people and that they have all their times here. So they're means 1 17.34 stated aviation 2.465 seconds. And if the normal models approximate are appropriate, what percent of times will be less than 1 14 27 5? So, first of all, it's probably good to go ahead and build our normal model. So right down the middle should be your mean. That's the 117.34. Then we'll have our 68%. So you'll then subtract the 2.465 that's going to get us the 1 14 0.875 which was part of the question. And then when you add 2.465 you're going to get 1 19 point 805 So just stopping there to answer officially Part A. It says what percent of times will be less than 1 14 So if this right here represents 34% then you have to do 50% minus 34%. That's gonna leave us with 16%. If it's below that, what is the actual percent times lesson 1 14 So then you go and look at your table and you count all the ones that were won 14.8 or 815 or less. And you've got a lot 1 14.8 twice won 14.71 14.6 on 14.51 14.4 twice and won 14.3. So you add all those up for part B, that's gonna be eight total out of the 59 that were listed. And so you do eight. Divided by 59. That's gonna be approximately 13.56 percent. So the two percentages don't agree. There's still a little bit of a difference. And so why, Um, what did they agree? And the answer is normal is not perfect. It's approximate. It's not perfect. Okay, so then you have to take the time to go and make a created his gram of these times. So what I did ahead of time was I went and I didn't put in all these times in my tea I 84 graphing calculator. So you do stat, So don't want to do this old calm right down the steps you go to stat at it. And your l one is going to have all of those numbers. All 59 numbers I don't know. Seems like a lot in your list. Then you go to stat plot and you select the hissed A gram option. And then once you set the history Graham option, you, uh, type the zoom button and then nine, which means it's gonna do the stat pot, the standard of that, and you be able to see a picture of your history. Um, so I'm gonna draw a sketch of the history, Graham. So you have a tall one here on the left, then it goes down. Then it goes down some more. There's a little bit one, a little bit above, down look it up of and then it kind of evens out and papers off around there. So, based off of what I see on this image, it's not normal. It's skewed, right? And so that kind of explains why it's not a perfectly normal situation.


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