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Seplemder Of zuuO, heart transplantation at St: concern that more patients Georges Hospital in London was suspended were dying in the last 10 cases at the hospital ...

Question

Seplemder Of zuuO, heart transplantation at St: concern that more patients Georges Hospital in London was suspended were dying in the last 10 cases at the hospital than previously: Newspapers reported that the 80% mc was of particular concern because it five - 2 stu average: Let the random variable Xrepresent was Over times the the number of deaths in ques Suppose Ithat the probability death random sample of 10 cases at this hospital is equal to the national rate of 15%. I(a) Identify the prob

Seplemder Of zuuO, heart transplantation at St: concern that more patients Georges Hospital in London was suspended were dying in the last 10 cases at the hospital than previously: Newspapers reported that the 80% mc was of particular concern because it five - 2 stu average: Let the random variable Xrepresent was Over times the the number of deaths in ques Suppose Ithat the probability death random sample of 10 cases at this hospital is equal to the national rate of 15%. I(a) Identify the probability distribution of X(both its _ name and its parameter values). (6) If p = 15at St George"s Hospital; determine the probability transplant that in cases" that at least 8 random sample of 10 heart would result in death



Answers

Work each problem. In a recent year there were 51.277 people waiting for an organ transplant. The following table lists the number of patients waiting for the most common types of transplants. \begin{tabular}{c|c} \hline Organ Transplant & Patients Waiting \\ \hline Heart & $3,774$ \\ Kidney & $35,025$ \\ Liver & $7,920$ \\ Lung & $2,340$ \end{tabular} Assuming that none of these people needs two or more transplants, approximate the probability that a transplant patient chosen at random will need A. a kidney or a heart. B. neither a kidney nor a heart.

So on this one we're given that the mean number of heart uh surgeries that they do per day is six. And we can see from this that this is going to end up being the poison distribution. And we want to find on the first month if you look at the next day what's the probability that it's going to end up or going to end up having the number of the seven? And so instead of using the because we can use the voice on formula and we can go through and take that's six to the power of seven and then the E. To the negative mean power divided by the X. To that value. But if we use our poison pdf and put in the mean and then the X. Value that will hasten our ability to find that answer. So let's see what we get when we do that are mean is six and that tax value is seven. And we find that probability comes out to be a 0.1376 Well rounded to eight. And then part be asked what's the likelihood that the number of heart surgeries will be greater than or equal to eight? Well we want to use the complement so it is going to be one minus the number being less than or equal to seven. And let's use our poison CTF you're looking and we can plug in the mean and the seven and make sure you have the CDF. So one minus. And then we'll go to distribution and get that CDF are mean is six and our number is seven. And that's going to add up all those values below and then take one minus and this becomes 10.25602 Then on part C. We want to find the probability that at most for And likewise we would like to use that poison Sadia because we want to accumulate and are mean is six. Yeah. Let me pull that up and Armenia six and our number is four. And make sure you again have the sea so that will accumulate downward. Always accumulates downward. All those cumulative buttons accumulate downward and 40.28504 I'll just rounded to six so there we go, all three answers.

30 Question eight Given an equal 10 probability equals 70% equal 0.7 The financial binomial probability is probability off X equal key equal N C k The people key that one minus be or in the minus key equal factorial in over factorial key Multiply boy factorial in minus key that be off a party that one minus B forward in the minus key Evaluate a key equal six, 78 nine, 10 Yeah, so even have probability off X equal six equal First Victorian 10 over. Factorial six Multiply boy Factorial 10 minus six No brain seven 46 The one minus 10.7 Our 10 minus six equal point to factorial x x equal seven Cool factory Elton over. Factorial seven are deployed Boyton minus seven Story in that 0.7 Power seven The one minus 10.7 or then minus seven equal Going to 668 Victorian X Equal aid equal factorial 10 Over factory in wheat multiply boy factorial 10 minus eight dot point seven or eat the one minus 10.7 or 10 minus eight. Equal 0.2335 Colonial. It's equal nine sequence Probability of X equal mine equal problem. Factorial 10 over Victorian line. Multiply poet in minus nine factorial good 0.749 but one minus 10.7 for nine or 10 minus nine equal 0.1 to 1 for the charity off X equal, Thin, equal factorial 10 over factorial 10 Multiply Boy T minus 10 factorial not 0.7 14, but one minus 10.7 14 minus thin. Equal 0.289 a. The correspondent probabilities And so the prosperity off X is bigger than or equal six is almost equal. 0.38 to 8. The financial conditional probability. The security off puree equal probability off e and B over probability Off e use it. Use it. The definition off the conditional probability prosperity off eight is less than or equal X over six is less than or equal x equal probability off it is. Listen with equal X and six Lesson or equal X over probability. Off weeks is living or equal X Equal probability off. Eight Is losing or equal X over probability off. Six. Less than or equal X Equal foreign. 382 over point 849 Equal or in four fine and it's equal 45% question number me given unequal 10 and probability equal 70% equal 0.7 we will use above creation off definition phenomenal and will weed 80 equal speaks 789 10. So we will have a probability off X equal six equal 60.0 a to probability of X equal seven frequent 0.26 Probability off X equal eight equal 0.23 and capability off x equal mind equal 0.12 Probability of X equal then equal point here to eat in the correspondent capabilities. So probability off X is bigger than or equal six. Equal probability off X equals six plus probability of X equal seven plus probability of X equals eight plus probability of X equal nine plus probability of X equal 10 Equal almost 0.8 Fine by using the definition off off. Conditional probability Prosperity off X equal 10 over six is bigger is less than or equal c x Equal probability off x Well, then, in six The reason or equal six over for prosperity off. Six Less than or equal extrude, it will prosperity off. It's equal tonton over ability off six is less than or equal X equal 10 to eat over 0.84 nine. It equal almost 0.33 equals 3.3 percent.

33. The resting heart rate for an adult horse should average about 46 beats per minute, with 95% of the data range from 22 to 70 beats per minute. So we have a range of 22 to 70 based on information from the Merck Veterinary manual, let X be a random variable that represents the resting heart rate for an adult horse. Assume that X has the distribution that is approximately normal. All right, so we have 95% of the data. What that really tells us is on our standard normal curve with Armenia, 46 95% of the data is between 22 70 which has just given us what that second standard deviation is, or how far the second center deviation would be away from the mean. So we can figure out the standard deviation by looking at the gap or the distance between 46 70 and that distance is 24 and there's two standard deviations that spread out from 46 to 70 and that tells us that one standard deviation is 12, which is essentially our spacer, and we can insert 58 as one standard deviation to the right, and 12 minus 46. 34 as one standard deviation to the left. Now, once we have this complete information, we can go to our questions A says, estimate the standard deviation of the X distribution and we did this already because I wanted to complete my curve and we have that standard deviation being 12. So our estimate here is 12 B. What is the probability that the heart rate is fewer than 25 beats per minute? Well, if we're looking at our curve, we want to find the probability that a heart rate is fewer, then 25 beats per minute. We want to identify her 25 years on the curve, 25 is somewhere between negative one and negative two. Standard deviations from the mean. And I want to shade in everything that's fewer than 25. So essentially I'm looking for that shaded region, R T i 83 or 84 calculator allows us to find this by using the normal CDF command. We want to know what is the lower region or what is the lower bound. Um That is where does the shading start? Well, essentially it starts at negative infinity because the curve never touches the axis, but our calculator needs to see it as negative 999 The upper bound is where the shading stops. We're going from negative infinity to 25. That's what you see represented here, inserting the mean and then our estimate for our standard deviation. And once we do this we can type that in and we get zero 0.0 for 01 All right. See what is the probability that heart rate is greater than 60 beats per minute. So I'm going to send to the same process here, but we want to find 60 which is just outside this first inter deviation. And I want to know everything greater than this. I'm looking for the shaded region and purple this time. So I can go back to my normal CDF command again. I want to know my lower upper mean and standard deviation this time. My lower bound is where I start shading is at 60. My upper bound technically goes to infinity, but my calculator won't accept affinity. So we're gonna insert 999. We have the same mean the same center deviation and that purple region is 0.1217 D. What is the probability that the heart rate is between 25 60 beats per minute? So the probability of the heart rate, the X is somewhere between 25 60. So what we're doing here is we want to find this green region. The space between 25 60. We can still use this normal CDF command are lower bound is where the green starts. It starts at 25.

Total number of people. Total number off people is equal to 51 77 Now, the first part of the questions is probability Me? Oh, it high. So we know this will be will probably take it me. Plus, probably be hard. Minus probability killed me. Intersection Heart. It's given in the question all really the data. Zero number of people who need the warm or transplants. So intersection part would be zero No, probably a kidney is equal to 350 to 5 upon five, 277 plus probably the hardest. 3774 upon 51277 So this would be 997 838799 upon 51277 No, the second parts is me. That after me neither kidney, no hot. So this will be probability. Give me dash in. Dissection. Hi. Dish. We know from the Morgans know that this would be equal to probably take it me Union. Hi bash. So this would be equal to one minus. Probably deep give me union heart, which we have calculated in the force part. So one minus 38799 upon 51277 So this would give us 500 to 77 minus 38799 upon 500 to 77 This would be equal to 5.277 and 38799 So 76 17 minus nine is 345678 Again, he carries a 16. Minus nine is seven 11 minus seven, Ford 10 minus 82 and one. So this would be 12478 upon 512 77


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