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Ages of first-time mothers in 2013Age 14 1622 #...

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Ages of first-time mothers in 2013Age 14 1622 #

Ages of first-time mothers in 2013 Age 14 16 22 #



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The rates of teenage births are reported as the number of births to mothers age 15–19 per 1,000 people age 15–19 in the state. Shown below are the mean and standard deviation of teenage birthrates for all 50 states and the District of Columbia, for Hispanic mothers, Non-Hispanic black mothers, and Non-Hispanic white mothers. The lowest rate for Hispanic mothers, 31.3 births per 1,000, occurs in Maine. The minimum for Non-Hispanic black mothers is Hawaii with a rate of 17.4 births per 1,000, and the minimum for Non-Hispanic white mothers is the District of Columbia with 4.3.

Let's take a look at our function. F of X equals negative. 0.198 X squared plus zero 0.1054 x plus 12.87 Well, by examining my function, I see that I have my highest degree. Term is an X squared term. That means I have a parabola. It is a negative coefficient. So it is a downward facing parabola. So my vertex is showing me the maximum value for this function. But what is that? Maximum value? What value of X gives me my maximum results? Well, to find that out, I need to find the Vertex. So I need to complete the square every term with an X in it. I'm going to put together every term without an X. In this case, 12.87 I'm going to set over to the side now just a notice. We go through this problem, the final result we're gonna be rounding to the nearest 10th But I don't want to round too soon. If I wrapped around too soon, I could introduce a lot of rounding error in my final answer. So throughout this problem, I'm going to carry 4 to 5 decimal points, and at the very, very end, we will round the appropriate number of places. So I need my X squared term to have a coefficient of one. So I'm going to factor out negative 0.198 from every term with an accident. So that gives me an X squared minus 5.3 to 3 to 32 x again. I'm carrying several digits. We will round it appropriately at the end. I'm gonna give myself lots of space in these parentheses and that 12.87 will sit over there by itself. Now, to complete the square, I take a look at the coefficient of my ex term on. I want half of that. In this case, that's going to be negative. 2.66 1616 and I'm going to square it. That's the number I'm gonna put back up inside my parentheses to complete the square. That would be 0.7 Sorry. 7.8 for two. Now, I can't just add a number to a function, so I will also subtract 7.842 by adding and subtracting the same number. I haven't affected the overall value of my function. So the pieces I need to complete the square Our X squared minus 5.3 to 3 to 32 x and the 7.8 for two. I would like to move this number outside of the parentheses, but don't forget, everything in the parentheses is being multiplied by that coefficient in front. So when I move it outside of the parentheses, what I'm really moving is plus 0.140 to 7, and I'm gonna add that to the 12 point 87 that's already out there. So if I write this with my perfect square, I get X minus 2.661616 squared. Plus, when I combine those two numbers on the outside 13.1027 So from this I confined my vertex. It happens at 2.661616 13.1027 So what does his Vertex tell us? Will The X value is how many years I am past 1990 and we should round down for the year. So if around this down. I get a two. So my eat my excess, too. Which means my year is 1992. The Y value is the output of my function. It's the percentage that I'm looking for. I need to round this to the nearest 10th so that gives me 13.0% as my maximum value for this function.

So here we have a graph representing the number of births from teenage moms age 15-17 for selected years starting with 1980. And it wants to approximate the intervals over which the number of births from teenage mothers increased. So it looks like we have an increased from about five 2 15. So that would be from 1985 1995. And then it also looks like we have an increase from 25 to The end of 27. So that would be yeah 2005 To 2007. That was for a now for be approximately the intervals over which the number of births from teenage numbers decreased. So that would be from 1980 to 1985. And from 2005. Sorry. Now from 1995 to 2005. Mhm. Now she wants us to estimate the values of any relative maximum or minimum. So for c these are thousands. Remember It looks like we have a relative minimum right here. 12345. So in 1985 200 1000 first In 1985 I'm sorry not 200,000. That would be about C- 160,000. And then for maximum It looks like almost 200,000. Mhm mm. In 1995. And then it looks like we have another minimum about here. So that looks like it's gonna be 2004 or 2005. Um about 125,000 In 2005. So that would be all the mens and max is so far in that.

Right now, we're looking at real world data and how it compares to our normal distribution were given a chart here that describes the age of women. Um, who gave birth for the first time within a calendar year. So first, it wants us to sort of make a hist a gram out of the relative frequencies from this table. So to do that, we're going to find the relative frequencies in this table. Um, first, we do that. We want to add up the total number of observations in this table. When I do that, I got a number, um, four million 71,111. And now we're going to go through each entry in the table and just divide the count by the total to get a relative frequency. So women between 10 and 15 made up 0.1791 of total women giving birth 15 to 20 0145 20 to 25 was 0.2511 25 to 30 0.26 05 30 to 35. 0.2337 35 to 40 was 01115 run out of room here. We've got 40 to 45 being 002353 and then 45 to 50. It's going to be equal to 0.1348 So now we have the relative frequencies of each age group and we want to plot this in history. Graham. So I'm going to draw our X axis here and we're sitting at 10, 15, 20 25 30 35 40 45 50 and four. It should be a 10. And then I'll draw a sort of Y axis over here, and we see our peak is at 0.26 We're gonna write right here. It's going to be 0.25 Well, sort of break it up into fifth. I want you. Yeah, that's about fifth. And that will be our scale for our history. Graham. So let's start drawing between 10 and 15. We had a number that's so low that it barely registers on our history. Graham, don't just draw it like right there. It's very, very small, Um, 15 to 20.1045 So that's going to be about right there. 20 to 25. We were at 0.25 So I'll draw that about here. 25 to 30. We were at 0.2605 So I'll draw that just a little bit above right there. 30 to 35. We went down to 0.23 so that's gonna be a little bit below right about there. Yeah, 42. They're 16. 35 to 40. We have 0.1115 So it's going to drop down again about right there, Sort of an estimate. Again. This is not going to be perfect, but it'll give us a good idea of what the state looks like. Then 40 to 45 0.230 point 02 Excuse me. 353 Which would be about there and then the last bit will be half of that 0.1 So right there. And if we draw our blinds now, we'll get something that looks a little bit like this. And that was going to be that is going to be our hissed a gram. And so what can we say about this? this. The next part of this question wants us to say, Is this normally distributed data? How do we know? Well, but if we drew a normal curve here, we can say that this data is centered around. Somewhere in the 25 to 30 range would have the center about here. We can also see that it's pretty symmetrical as we go, Uh, distance X in the left direction were brought down to about here. And that's the same as if we go distance X in the Y direction. It's pretty close to it. It's a good approximation of symmetry, so we know that it's, you know, model. It has one peak and it's symmetric, and these are two key things about our normal distribution. We can also see that as it goes further into the wings, it gets closer and closer to zero. But it doesn't, of course. Of course it goes down to zero at some point because we're dealing with a finite amount of data. But it sort of has that wing shape where it goes like that. So if we were to superimpose a normal curve over this data would look something like this and As you can say, it's it's approximately normal. The data we're working with is almost normal. So we can say that, yes, this is approximately from a normal distribution, and that is your final answer.

Alright in this problem, this model represents the number of babies born to teenage mothers and our job is to figure out in which year was this number the highest. Okay. Remember we can find the vertex of a parabola by using the equation X equals negative B. Over to Hey, you might be thinking I don't see a B. I don't see an A anywhere. But we always need to reference back to the general form Y equals a X squared plus B, X plus C. Okay, so now we know that x equals R. B. is the coefficient or the number in front of the extra. So that's going to be 2.75 times are over two times A and the A is the coalition on the X squared term or that square term. Okay, so two times negative your .7-1 and let's see what this ends up being so negative 275. And then in the denominator .7-1 times two this is going to be negative 1.4 42 And we do this division we get 2.75 divided by one 442 This is going to be about one 91 Okay, So 1.91 is going to be our X value. Okay. And the only other thing is to figure out how many babies were born in that year. And we're going to substitute this value back in for an O. T. But instead of tea You're going to use the 1.91. Yeah. Okay then we are going to substitute 1.91 every time we see a.t Into our original function. So negatives Europe .7-1 71.91 squared Plus 2.75 Times 1.91 Plus 500 and Toning eight. Okay, after this substitution we get very very very close to 530. Okay. So we did a lot of math to get a ordered pair. Are x coordinate. Remember is going to be that 1.91? And are y coordinate is 530. So what does all this mean? So are 1.91 r. x coordinate. This is the number of years after 1989. Okay. So that means the year with the highest number of babies born 18 months was 1.91 years after 1989. Okay. So we could go one full year to 1990 and then almost another full year to 1991. Okay, so in 1991 about 530,000 babies were born in this category. That was the maximum according to this.


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