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The average retirement age for cenain county was repored be 56. years according an intemationa group dedicated promoting trade and economic growth With pension syst...

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The average retirement age for cenain county was repored be 56. years according an intemationa group dedicated promoting trade and economic growth With pension system operating deficit. bill was introduced by the goverment during the summer raise the minimum retirement age from 60 to 62. Suppose sunvey 38 retiring citizens taken investigate whether the ne" bill has raised tne average age at which people actua Tete Assume the standard deviation of the retirement age years . Using a = answer

The average retirement age for cenain county was repored be 56. years according an intemationa group dedicated promoting trade and economic growth With pension system operating deficit. bill was introduced by the goverment during the summer raise the minimum retirement age from 60 to 62. Suppose sunvey 38 retiring citizens taken investigate whether the ne" bill has raised tne average age at which people actua Tete Assume the standard deviation of the retirement age years . Using a = answer parts through belu Type can occur when the researcher concludes the average retirement age ncreased tne average reltirement age did not increase when facl; Ihe average rebirement age increased but the average retirement age did not increase Type eror can occur when Ine researcher concludes that Calculale the probabillty of a Type (nan occuring the actual population age The probability = commitung Type Arno 0.674 (Round t0 three decimal places as needed ) Calculate the probability of a Type elor occufnno if the actual population ag0 years old. The probability commiung Iype Giror (Round three decimal places as needed ) yearg



Answers

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of $1851,$ we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. $$\begin{array}{|l|lllllll|} \hline \text { Age range (yr) } & 20-29 & 30-39 & 40-49 & 50-59 & 60-69 & 70-79 & 80+ \\ \hline \text { Midpoint } x & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 & 74.5 & 84.5 \\ \hline \begin{array}{l} \text { Percent of } \\ \text { nurses } \end{array} & 5.7 \% & 9.7 \% & 19.5 \% & 29.2 \% & 25.0 \% & 9.1 \% & 1.8 \% \\ \hline \end{array}$$
(a) Using the age midpoints $x$ and the percent of nurses, do we have a valid probability distribution? Explain. (b) Use a histogram to graph the probability distribution of part (a). (c) Find the probability that a British nurse selected at random in 1851 was 60 years of age or older. (d) Compute the expected age $\mu$ of a British nurse contemporary to Florence Nightingale. (e) Compute the standard deviation $\sigma$ for ages of nurses shown in the distribution.

We're looking at the mortality table, and our first question asked us, What is the life expectancy of a 67 year old female? And if we look at our table for what the life expectancy is, we find that it says the life expectancy column for that age group comes out to be 17.95 So then we would in round that off to 18 years, we would expect a female who is 67 years old to live 18 more years. That's what we would expect now. Part B asked us a question a different way. We want to know what is the age that we expect for a man who is 56 years old, so a 56 year old male? How long do you expect that mail to live? And so if we look at the column for life expectancy, we see that the life expectancy is for him to live another 23.52 years, which we would round that to the nearest integer. So for 24 years and then add that to the 56. So we would expect him to live to an age of 80 years old. So that's his age, as opposed to this is how many years longer you expect this woman to live now. Part c asked us, um, if they ensure 20,000, so 20,000 people are insured who are 69 year old females, and we want to know how many of them would die. So we want to know what number would we expect to die by their seventh birthday? And if I look at this column or this row for a 69 year old, we have the probability of death, and then we have a life expectancy, and the probability of death for that group is 690.16651 That's the likelihood someone will die if they're 69 years old, a female, that's the likelihood of dying. And we know we're going to give those policies out to 20,000 people. And so we multiply those together and rounded up to the nearest energy. We would expect 333 of those females to die during that year of being 69 before their 70th birthday. Now we do the same thing for a category of man and for the men. We're looking at 59 year old males, and we have 14,000 people who are going to be insured. And so we want to look at what is the probability of someone dying when they're 59 males? And the probability of dying for a male is 0.108 27 So that's the likelihood of a male who's 59 will die during that year, and we're going to have 14,000 people who are insured. And so the product of that is how many you expect to die and rounded off to the nearest integer. We would expect that many men to die 152 now just applying same principle. Except this time we're doing it for a generic number of X, and we know that we have a 61 year old female. And so we look at the probability of a 61 year old female dying, and we find out that that probability of death is 0.8187 Now what are we going to do with that number? We're going to multiply it by how many women we have ensured, and that is X so that product is our answer. And then the last question asked us. What is the probability that a 60 year old male will live? So it's reversing, finally talking about living to be 61. And so we look at the probability of a 60 year old dying, and that death is 600.11858 and then we want to find that's dying. So living is one minus that. So the likelihood that a 60 year old male will live to the next year is 600.988142

So we can see the table here. That is the age in the prophet. Oh, so the probability So, Adri, How 21 22 23 24. And if I, when you call a lot driven 26. So for the fourth year, do some one by 21 Rick Crawford. Well, bury my notes of 100 Sultan's plus 250 that ihsaa money that person paid for the first year. And also for the second year, we need to plus another 220 again, not there to hang greed and 30 year olds. You rode your role the other one so that it's a fright. And if the person rather than by for those years the profit will be to Hendry and comes well, 300 for a coupon fraud and the probability here we got all those probability. And for this one, the little P here thus equals one miners The rope on zero to your old 183 rhinos 0.186 rhinos point 00189 Miners 0.1 night one 193 Reach Yukos who point Sinai zero for out eight. And those offered exactly. While we know that equals who each profit hums each probability off it. So we can God, uh, Miyu here, just you call. So 303 0.35

In this problem, we are given some statistics about the growth of elderly population around the world. And we are being asked to calculate a couple of probabilities about um the aging elderly population. And so basically you're going to want to start by familiarizing yourself with the table. Were given North America and asian numbers as well as the ages of these populations and were given them as the percentage of the population. Yeah. So to start in part a you're being asked if three people are chosen at random from North America, what is the probability that all three are 80 years old or older? And so just by looking at this church, um the probability that three north americans are older than 80 is equal to the probability that one north american older than 80. Yeah. Which is To the 3rd power. Which as you see on the table is 3.3 Um to the 3rd power. And this gives you um 0.00359%. In part B were being asked to find what is the probability That if three people are chosen at random and Asia that all three are 80 years or older and so we repeat what we did in part A and find the probability that three asians are older than 80 which is equal to the probability that one asian is older than 80 Which is equal to to the third power. Which as you see in the chart is your .8 to the third power. Your .2 to the third power. And if you multiply this out Or if you do the exponents that is about 0.0000512 of the population in part C. Okay. We are being asked if three people are chosen at random from North America, what's the probability that the first person is 65-70 for the second is 75-79 and the third is 80 years or older. And so to find the probability of this, we would simply multiply the probability of these three events happening. So the probability that a North American is 65-74 Times the probability that a North American is 75-79 Times the probability that a North American is greater than 80. And if we multiply these together, we get 6.6 Times 2.7 % times 3.3%,, Which is approximately 0.0000058 heat Or, 0.00058 8%. And part do you have this question is asking um whether this sampling occurred with replacement or without replacement. Um And in parts A to see, we assume that the events were independent and that sampling occurred with replacement. Um However, it doesn't really make that much of a difference whether the sampling occurs with or without replacement when the population is extremely large compared to the sample, and so the probabilities aren't strongly changed because we selected an individual already. Yeah.

Hello. Today, we're gonna be working on a probability problem on the right hand side here we have our table. Um That gives us the age of, I believe, yeah, male age every 10 years. Um for 100,000 males. Um So our first question is, what is the probability that a 40 year old man will live to be, will live 30 more years? So the way that we will do this is we look at the table, we say, okay, the number of people that are 40 is 95,889 and 30 more years. That means 70 the number of people that are 70 r 73,355. So what we want to do is we want to take um the total number of seven year olds divided by the total number of 40 year olds. And this will give us the probably the number of 40 year olds that live 30 more years to be 70. So this gives us uh 73,355 divided by 40 is 95,000 889. And when you plug that into a calculator, you end up getting 8890.765 is our answer for a. So for bebe they're asking, what's the probability of 40 year old man will not live 30 more years? Um So if you don't live 30 more years, that means you're not going to live to be 70. So if this is the probability that we live to be 70 then the probability that we don't live to be 70 is just the the complement of this. So it's just one minus 10.765 And that gives us a point oops 0.235 235 So this is our a answer. This is our B answer. Yeah. Uh huh. So now for c consider a group of 5 40 year old men. What is the probability that exactly three of them survived to age 70? So we have 5 40 year old men, three of them live to age 70. So this becomes a binomial probability. So we're going to utilize this um formula. So by normal probability is the number of combinations times the number of people that are fulfilling whatever the condition that we have, times the number of people, excuse me, times the probability of the people that don't fulfil the conditions. So this is the probability that people fulfill the conditions is the P. D. X. And the probability of people who don't fulfill the conditions are Q. Times raised to the n minus X. An end just being the number of people X being the chosen number. So in this case are uh number of combinations is going to be five two's three times the probability that um 53 of them survived A. G. So the probability of a person that is 40 living um to age 70 is the 700.765 that we found in A. And we are going to raise that to um the raise that to the third and so and minus X. This is going to be raised the second because remember we have 53 plus two is five. Which means that five minus three is two. Uh And in this case this is the probability of people who don't fulfill the condition of people who don't live to 70 from age 40. And in this case is going to 400.235 So that's what we got for. B. Yeah so in this case what ends up happening is five choose three ends up being 10. And when you multiply these together you get 0.0 to four um seven 247 Yeah. And so the answer ends up being 0.247 Yeah I see the answer now for D. You are considering to 40 year old men, what is the probability that at least one of them survives to age 70? And the hint that they give us is the complement of at least one is none. And so in this case we want to say, okay, what's the probability that um someone that we have? Two men and neither of them live to age 70? So the probability that somebody does not live to age 70 again is RB answer it's 700.235 And so for D we end up having is 0.235 35 squared because there's two men which gives us zero 552 And then because we're looking for at least one man which is the complement of uh neither of them living to that age, we do one minus 10.552 And that gives our answer to be 0.9 for five. If you round up. So five is not very good. 0.945 that would be our answer for Dean. Yeah. Yeah. So again, um most of these are just basic probability. The only like kind of tricky one was at least for me, was the binomial probability that comes with C mainly just remembering this formula, remembering this uh and choose X. That you're gonna have to multiply everything by and then you should be fine, awesome.


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