5

P 8200 11300 12500 14400 16100 18900 B(P) 0.49 0.50 0.52 0.48 0.49 0.51 PS(P) 3345 4554 5125 6147 7184 9144Table 1: Birth rates B(P) and death rates PS(P) at kuown ...

Question

P 8200 11300 12500 14400 16100 18900 B(P) 0.49 0.50 0.52 0.48 0.49 0.51 PS(P) 3345 4554 5125 6147 7184 9144Table 1: Birth rates B(P) and death rates PS(P) at kuown values of the population P.6. Thedata ou the birth uudl death rates B(P) aud S(P) of this_ uc showa in Tablc 1. Usc Icgrcssiou to cstinatc population then find 6(P) . Determine +bo wel B(P) aud PS(P) , ad

P 8200 11300 12500 14400 16100 18900 B(P) 0.49 0.50 0.52 0.48 0.49 0.51 PS(P) 3345 4554 5125 6147 7184 9144 Table 1: Birth rates B(P) and death rates PS(P) at kuown values of the population P. 6. Thedata ou the birth uudl death rates B(P) aud S(P) of this_ uc showa in Tablc 1. Usc Icgrcssiou to cstinatc population then find 6(P) . Determine +bo wel B(P) aud PS(P) , ad



Answers

BIRTHS AND DEATHS


In Exercises 67 and 68, use the table,which shows the total numbers of births $B$ (in thousands) and deaths $D$ (in thousands) in the United States from 1990 through 2006. (Source: U.S. Census Bureau)

The models for these data are
$B(t) = -0.197t^3 + 8.96t^2 - 90.0t + 4180$
and
$D(t) = -1.21t^2 + 38.0t + 2137$

where $t$ represents the year, with $t=0$ corresponding to 1990.

Find and interpret $(B - D)(t)$.

And question members of the team. The correspondent distribution is a possible distribution. We cause on average rate is given. That is not, ah, probability for which you would use by a longer distribution. So the average rate is the burst on death, right? So have a drink for birth effectual 16, and I would rate for death. You going to eight? The point to me from from the results of part eight to get the formula off. So this probability it's me when X equals okay, Because you want the ball. Okay, Law, easily me because longer over characterization came to evaluate. Okay, Equal to 10 and 16 for the you're anxious for Q and X equal to 10 in 13 16 4. Okay, by equal or negative 16 over secularization 10 Well approximately equal. 4.4, 304 to 1 one x equal to 16, he says to me. 16 for 16, Boy in power native. 16/16 Fact tradition approximately equal or going to fall 900 92. Do you You really leave okay equal to 10 and 16 for this for fuel and executed them is listening. Eight important boy people needed. Eight overtime factor. Positional approximately equal or point on. Plus 190 history. Thank you, Mr. It's equal to 16 is equal to eight for 16 by even with Mrs Eight over a position. 16 for equal to before you two doubles. All 45 in part C from the results of part A. We have a community off 1000 and 1500 people and stayed okay of thousands people. That's the ring. Have to be multiplied by 1.5 that we did it for me. Why did $101,500? I'm sorry. So Lando's girls thank you too. 16 by 1.5. It could 24. Wonderful. That's you said to me eight boy, 1.5. You can do 12. You know, that course of capability is when I speak. Okay. You thank you from the bullet. Three by people in need of wonder Over characterization came Do you want to? Eventually that came is taking 10 and 16 company from human Exeter to tend to see if you to 24. Um, 10 more people need to 24 over fact transition can will affectionately thank you whole point. Strictly old. 660 when he you And actually 4 to 16 people See 24 for 16 by evil. Negative 24. You've got a good voice. Mhm Christ proposition. You're not functional. Difference We're going to for 200 19. You want to evaluate? Okay, Equal to 10 and 16. But for this. So if you want X equal to 10, you could do okay. All of them by the phony. Just 12 over factory ization can all approximately equal opening. 20,000 and 48. Everyone exits later. 16. Did you say to me? 12 for 16. Why you following? Negative close over for actualization. Sustainable Welcome, sweetie equals 4.4, 543 And point Dean, from the results, we have some Part eight. We have the community. Well, 750 people instead. Oh, saw them people. But the rains have to be multiplied by I'll find saving to five. So among the first we're equal for 0.75. Boring 16 is equal to 12 a longer for this people to open 75. Boy Kate is equal to zero. We know that formula. What's so Mr Bush in probably when X equal to came in control from the follow came while in politics of London over a transition came. You won't do you benry February at the game people to then and 16 home That and for Okay, okay, we have one x equal to 10 easy questions. 12 for 10 R E or negative 12 over 10 Characterization with approximately equal opening 1000 and 48 when he X equal to 16 is equal to 12 for 16 by installment of 12 over Spectra, Position 16 and approximate People four point 500 Reporters Street. That's for versus for this 20 x equal to 10. A question 64 Thin by you, Barney because so over that transition tell will approximately equal oh point all 413 24 x 7 to 16 Is it for two, six or 16 by people in the six or factories? Asian 16, while approximately equal to four point Tripoli. All 334. Thank you

So this question were asked to describe the sampling distribution of the sample proportion. So first we check for two conditions, we check there are no sample is independent. So for that we need to make sure that the sample size, It's less than R equals 2.5 times 25 1000 it is. So this is independent. And then we check MP 1 -2. So we checked that there is a large enough sample size, make sure it's approximately normal, so mp one minus peace and P one minus piece or 300 times 3000.7 times 0.3 is 63 which is more than or equal to 10. So we can safely conclude that the sampling distribution of Jihad as an approximately normal distribution with the mean of the sample proportion equals two population mean And the standard deviation is equals two. Basically P one -P over in square root of the whole thing. So .7 times .3 over 300. Get rid of that is approximately 0.0-6. Hi, so we have an approximately normal distribution with mean and standard deviation

We have B A T, which represents the number of births in the United States. In the thousands, starting with T equals zero in the year 1990. We have D E A T, which is the number of deaths in the thousands. And in the last problem, we found the equation for B minus T, which is the number of births minus the number of deaths. So that would be the population growth for the year. So in this problem, we're going to find the population growth and the number of births and deaths for the year 2010 on for the year 2012. So we're going to use T equals 20. For the year 2010 we're going to find be of 20 de of 20 and B minus t of 20. And this is a great time to use your calculator, type these functions into your wyffels menu and then use your table to find the values so that you don't have to do as much number crunching yourself. So in the year 2010 when T equals 20 the number of births was 4388. Remember that 1000 and then the number of deaths was 415,000 on the difference between those is 1975. So this is the number of birds in the thousands in that year, the number of deaths in the thousands that year. And so then the difference would be the population growth that year. So then we can repeat that process for the year 2012 by using T equals 22 go back to your table and put a 22 in there, and we end up with 4439 1000 births. 2384 Excuse me, 87,000 deaths and 2000 approximately 2051. 2052 1000 in population growth.

So this question were asked to describe the sampling distribution of the sample proportion. So first I checked for normality, we check for independence so we take .45 times and That gives us 1250 and we c. n. is less than or equals to end. So the samples are independent. And then we check for the sample size so we take and mm one minus P. So that's and I'm please times one minus Mhm. So 1 -13 is .897 times 1000 times point one of three gives us 92.4 which is more than r equals two tens or sample size condition is also satisfied. The sampling distribution of P is and approximately normal distribution with the mean of. He has close to team and the senate activation of jihad is basically or to the square root of When one or 3 1.897 over 8000 so .1 or three times 1 -1 or three over 1000 taking the square root of that. We get value of approximately cyril 0.1. So we have an approximately normal distribution with mean and standard deviation


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