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[nonPauicie Hanela Gatg Chrom _ mathxl: com/Student Playertlomework Knom wolId -5376684488q tnnld flushed- Business Statistics Ialseucid 56221028centerwin (BBA 403)...

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[nonPauicie Hanela Gatg Chrom _ mathxl: com/Student Playertlomework Knom wolId -5376684488q tnnld flushed- Business Statistics Ialseucid 56221028centerwin (BBA 403) Fall 2019 Patricla Herrera 9/14/19 5.19 Homework: Homework Week One Chapter 6 - Section 6. Score: 0 of 4of 15 (3 complete) HW 6.1.11 Score: = 2038, 3 of 15 Use the Vatues Question Hepp the number Fne find Ihe sampling ertorStThe samnpling error IEnier Voui Joserans €anc Inen cllck ChzckAIl parts showing

[non Pauicie Hanela Gatg Chrom _ mathxl: com/Student Playertlomework Knom wolId -5376684488q tnnld flushed- Business Statistics Ialseucid 56221028centerwin (BBA 403) Fall 2019 Patricla Herrera 9/14/19 5.19 Homework: Homework Week One Chapter 6 - Section 6. Score: 0 of 4of 15 (3 complete) HW 6.1.11 Score: = 2038, 3 of 15 Use the Vatues Question Hepp the number Fne find Ihe sampling ertor St The samnpling error I Enier Voui Joser ans € anc Inen cllck Chzck AIl parts showing



Answers

(a) find the mean, variance, and standard deviation of the probability distribution, and (b) interpret the results. The number of school-related extracurricular activities per student $$\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Activities } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Probability } & 0.059 & 0.122 & 0.163 & 0.178 & 0.213 & 0.128 & 0.084 & 0.053 \\ \hline \end{array}$$

Problem. 1 13 says 25 randomly selected students will ask the number of movies they watched the previous week. The results are as follows. Find the sample mean question a and question. Be find the approximate sample. Standard deviation is so to get our example mean you basically multiply each data points by the frequency, Then add all those numbers up and divide by the total number of observations. So we had 25 observations, and they were five students who watched zero movies. So five times zero is zero. There were nine students who watched one movie, so nine times one is nine and there were six students watch two more reason for six times, too. Excuse me six times too 12. Then you just repeat that and at all those numbers up and divide by the total number of observations or the total frequency, which is 25. Then you'll get sample mean of 1.48 and not education. Standard deviation. You use this formula over here, which is the some of the deviations from the mean. So you would take each data point, then subtract the sample mean off vamping for eight, and then square that all right with that? For each and every observation. So from observation one a pencil. Observation 25. You subject the sample mean, then you square that difference, and then you divide by. That's also a number of observations, which is 25. So after you add all he was great deviations. We divide by the total number of observations which is 25. Then you take the square roots of that should give you an answer off 1.12 Thank you.

This problem covers constructing normal probability plots and determining information from them. So, to construct a normal probability plots from this data and this data is on south Carolina's Cisco abstract um about the daily charges in 15 hotels, so and equals 15. So this data, there is 15 different terms corresponding to this end. We want to find table three with the number 15 because we want to construct a normal um probability plot. So these are the normalized values. We want to first organize our data into increasing order. So what I would do is I would and put these values in a calculator and sort list. So you get the lowest values and the highest values right in increasing order and the corresponding um table three lowest values and the highest values right here. And it looks like the lowest value here is 47.72 and the highest value is 130 0.17 So 47 72 and correspondingly 3.17 and all the in between also had the same pattern. So once you have that, you can graph it, you can graph the X and Y. Of these things. And once you grab the X and Y, the plot will look something like this. And you can generally see the trend follows this line right here, right? It follows this line. We can determine if there is any outliers outsiders. So an outlier is when is points that don't follow a trend. So at this point, that is just true, for example, would not follow the trend because it doesn't fall into this line generally. But in this case there is no outliers because all the points fall into the line, so there's no outliers. And finally, if this trend is linear, right? If it goes into a line, then we can say that it is normal. Normally distributed. Okay, Only shredded pot. Okay, Yeah, right. If it wasn't um linear, then it wouldn't be normally distributed.

So in 1 17, we have a table that shows the results from 25 randomly. Slightest. Students asked the question, How many movies did you watch the previous week? So we're given X to be zero through four and the frequencies we got? Five. None 64 and one. Uh and then we have two questions. Question number one is to calculate. They simple mean in order to catch that simple mean I'm gonna go ahead and take this table a little further, and I want to find the relative frequencies, which is basically turning all these into a percentage. We know there's 25 total people that rest. So for zero, we have five out of 25 which is point 20 five out of 25 is 1/5. 1/5 is 0.20 So for nine, I want nine out of 25. That gives me a 0.366 out of 25 gives me a 0.24 four out of 25 0.16 and one out of 25. This 0.4. You can double check your work by adding up all of the relative frequencies that should be 100% or just one. All right, So to find the sample mean we're gonna take the summation of every single X value with their probabilities. So what? This means we're gonna take zero, multiply its probability or relative frequency. It occurs 20% of the time, plus one times +36 plus two times 2.24 plus three times 30.16 plus four times point oh four. Adding that all together we get 1.48 which represents the typical number of movies for this group. Um, this is this is the average number for the 25 students. M b. We want to calculate the sample standard deviation, a sample standard deviation is thes square root of the summation of every X value minus the means we needed the mean earlier squared. Tom's each one of the probabilities so we can play this in zero minus the mean of 1.48 squared times. It's probability or relative frequency is 20%. We're gonna do that for all of these values. And that continues on until you finish up with X value of four. That gives you a sample standard deviation of 1.1

Okay, So the question here is to find the standard deviation off this set of data of students who took a test. And this is the set of data that shows their current the number of correct answers they got on the test right here. So in our first row, we have the occurrences in this case, the correct answers. And in our second world, we have the frequencies. So just the number of times that number of correct answers appeared in this sample of data. So, like, for instance, we have two occurrences now, wait. Two times six correct answers occurred one time, seven correct answers occurred three times eight crack answers occurred and so on and so forth. So we want to find the center deviation of this. Um, and because this process is very tedious to do on paper, um, or step by step with a calculator. I actually went ahead, use an online calculator, got what I needed. Um, but, uh, what I'm gonna do is instead, I'm going to explain this process that the calculator is using step by step. That way, it'll save us a lot of time, but I will still explain the process. So you understand? Okay, let's get started. So first we take our two rows and we put them into ah table. Like so This is the first row right here, and this is the second row. And then what we do is first you want to find the mean s. So what we do is we take our frequency and we multiply by each number in our data set. So there's two occurrences in to talk. Yes, two occurrences of six. So it's 12. Ah, one occurrence of seven. So one time, 7 to 7 and so on and so forth. That's how we get these numbers in this column right here. Then we add them up to get the total number of correct answers in this sample, which is 440. We divided by the total number of students or the total number of frequencies in this sample, which is 40 and we get that are averages exactly 11 tonight's number because it doesn't have any places after its decimal. It's good. We can actually do this on paper. Um, without likes having toe, you know, go with a lot of chaos with decimals. Anyway, let's continue um, we can take each of our numbers and subtract 11 from it because they go up by one. This is a fairly straightforward process. Six minus 11 is negative. 57 minus 11 is negative. Four et cetera, et cetera. And then all these numbers will take them all and square them to get this column right here. So negative five squared is 25 negative. Four squared is 16 and so on and so forth. Um, so finally, it Because we have varying frequencies, we want to use the frequency formula for standard deviation and variants. So we need to multiply each of these numbers by the frequency to get this last column right here. So 25 times to which is a frequency is 50 16 times one, which is a frequency for seven is 16. So on and so forth. That's how we get all these numbers right here again. These numbers are actually really easy compared to like the other questions in the book that we had to go through. Um, so you could actually do this on paper if you want to. Um, but again, because this is time consuming on my part. I'll just like I'll just show you, like all this data that you need. Um, okay. And then we get our total is 1 90 And because this is a sample, we want to divide it by, uh, you want a divided by 10? Just kidding. We want a divided by 39 not 10. I was looking at the mean for a second. We want a divided by one less than our total. So we want to divide it by 39 which is one listener total. And we should get 4.872 as our variants. Um, And lastly, if you want to get just the standard deviation, we take the square root of our variance to get our standard deviation right here. 2.207 And that is your answer.


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