Sample of data size 40 and the largest observation is 20. With P3o -5and P7o =13,If we modify the data by multiplying by 2 and adding 3. What is the new Pzo?Select ...

A sample data set of size $n=30$ has mean $x^{\wedge}=6$ and standard deviation $s=2$. a. What is the maximum proportion of observations in the data set that can lie outside the interval (2,10)$?$ b. What can be said about the proportion of observations in the data set that are below $2 ?$ c. What can be said about the proportion of observations in the data set that are above $10 ?$ d. What can be said about the number of observations in the data set that are above $10 ?$

We'll start this problem off by recording what we know, We know that N is 30, the sample size is 30, we know that the mean is six, and we know that the sample standard deviation is too what we don't know is we don't know the shape of the distribution, so therefore we are going to apply chevy chaves theory, and we'll start off with a basic number, like, and since we don't know the shape, we're gonna draw some crazy shape, and in the center of our number line, we're going to put our mean, and then we will count by standard deviations. So we'll add to read eight, we'll add two, we're at 10, we'll add two, were at 12, we'll go back to the mean, we'll subtract two, will subtract two, And we'll subtract two. So now Part A is asking you what is the maximum proportion of observations outside Of the interval to 10? So we want to be outside Of the interval from 2 to 10. So two is 2 standard deviations away from the mean And 10 is two standard deviations away from the main. So, since each boundary of the interval Is two, standard deviations from the mean? In each direction, We could apply, Chevy chaves the're um with a K value of two. Now chevy achieves theorem says one minus one over k squared, so we're going to have one minus 1/2 squared, Which would be 1 -1 4th, Which would be 3/4 Or 75%. So what we're saying here is that at least and this is a key item here, three quarters or 75% of the data will fall between to intent, so that means 75% of the data, or we should say At least 75 would be falling in that realm. So to answer our question, if at least 75% is between two and 10, then we would say at most 25% Or one quarter of the data. Mhm. Lies outside The interval from 2 to 10. So let's look at part B in Part B. The question is, what can be said about the proportion of observations that are below 2? Well, if There's at least 75% in here, then below two Can be at most 25%,, or we could say or at most one quarter of the data, Part C. What can be said about the proportion of the data that would be above 10? Well, yes, At least 75 falls between two and 10 than at most one quarter or 25 Can fall above 10. And then finally part D. This time, we're now concentrating on the number of observations above 10. So we already said the proportion, we said one quarter of the data and we said at most one quarter of the data Can fall above 10. Well there happened to be 30 pieces of data. So we could say one quarter times 30 Which would be 34 or 15 halves or 75 but we can't have half of an observation. So we would then have to say at most seven observations Will be above 10 And I chose to go down to seven instead of up to eight because if we did, 88 is more than one quarter of 30 seven, is that less than one quarter and we can go at most that value. So at most we can go 7.5. But since we can't go half we'd have to say at most seven.

So here we are going to see how many how many times the combinations appear in our data set and those combinations could be even. Hey, to be one be toe see even and see two. So you're going toe. See how many times these combinations appear in the data set and we're going to the stamp in that table so you can see that even appears five times in the data Sirte and it toe appears little time in the desert be even appears 11 times. Beato appears twice C two appears twice and see, uh, see, even appears tries and see two appears 10 times in their data set. So, like when we will calculate row totals and column totals and there are in total 13 ft off observations. Yeah, So then we will calculate row percentages by dividing every value by the row total. For example, for this, um, value, we even simply calculate five divided by 5 200 so you can see that. And for zero, it will be zero again. For this value, we will calculate 11 divided by 13 multiplied by 100 we will get 84.62 Similarly, to divided by 30. What if I have 100? We will get 15.3 years in. So then we will go one on calculating column percentages. So column percentages we can calculate as, for example, five Divided by 18 Multiply 100 will be 27.78 like rice 11 divided by 18. Multiply 100 will be 61.1 Way in salon. Yeah, now here we can see that when X is equal to a, it always relates with why equal to one whenever X is equal toe? A. It always relates with why one? Because there is no value, such as a two in the data set. Likewise, when X is equal to be most often, it relates with why equal to one? Here you can see that most often it relates to buy equal to one only 15% off their times. It relates to buy equal toe. Further, we can see that when X is equal to see most often it relates toe. Why equal toe here you can see that 83% off the times X equal to see relates to why equal toe Onley 11% off their times X equal to see relates to why equal to one

Problem number, sir, to serving. We can say that if you add on these things for your open their vengeance in the decades that so me values on do change why you were playing it read, you know, s so we have to choose So if you add occurrence into you of the vision in there that said and the values do change when you're spread, do

In question number 26. If we have that, the Santa size is equal to 30 and the center of the mature um, tells us that the company is normally distributed with me, so the mean is equal to 136 and the Standard Division is equal to 4.66 over square. Load off 30 were approximately equal to whole point 8 51 feet in the same question. If we have that December size, we could go to 45 on the central limit. Theorems tells us that the company is normally distributed with me, which, equal to 136 and signal overs relative and equal to 4.66 over spirit off 45 when approximately equal to open 6 95. He we know that the mean remains the same. But the center division decreases has the synthesized increases. And at the end of this question thank you