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A new start-up plans to develop new body temperature scanner that attached together with the hand sanitizer and the personnel details. The following table provides ...

Question

A new start-up plans to develop new body temperature scanner that attached together with the hand sanitizer and the personnel details. The following table provides list of activities that must be accomplished to produce the new body temperature scanner:Days Activity Optimistic Most Pessimistic Immediale likely Predecessors[0u30 2550 30100E35G 725 70 2030 20 25 7035 70 72D, EH25LKConstrucl drawing of appropriate network for these above listed activities: marks)(6) Determine the expected lime and

A new start-up plans to develop new body temperature scanner that attached together with the hand sanitizer and the personnel details. The following table provides list of activities that must be accomplished to produce the new body temperature scanner: Days Activity Optimistic Most Pessimistic Immediale likely Predecessors [0u 30 25 50 30 100 E 35 G 7 25 70 20 30 20 25 70 35 70 72 D, E H 25 LK Construcl drawing of appropriate network for these above listed activities: marks) (6) Determine the expected lime and variance for each activity. marks) Identily be crilical path and be expected completion time of" the projeet Determine the earliest start time, latest start time, earliest linish time, latest finish time and slack time (15 marks)



Answers

Body Temperature. A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is $98.6^{\circ} \mathrm{F}$. The results of the study by P. Mackowiak et al. appeared in the article "A Critical Appraisal of $98.6^{\circ} \mathrm{F},$ the Upper limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich" (Journal of the American Medical Association, Vol. 268, pp. 1578-1580). Among other data, the researchers obtained the body temperatures of 93 healthy humans, as provided on the WeissStats CD. Use the technology of your choice to do the following. a. Obtain a histogram of the data and use it to assess the (approximate) normality of the variable under consideration. b. Obtain a normal probability plot of the data and use it to assess the (approximate) normality of the variable under consideration. c. Compare your results in parts (a) and (b).

All right in this question, they are reevaluating is 98.6, really the average temperature of a healthy human being, which is really interesting. There's actually some recent articles on this, so if you're curious, feel free to go follow up check them out. So this is definitely quantitative data. I can definitely calculate the range and standard deviation here. So I'm using Excel because it's very easy to use for this large data set. You can just open it from the file, from your from your book. And um but the interesting thing about Excel, it doesn't have a formula for a range because they use range to describe, you know, like this is a three to a seven call that a range. So we've got to use the formula that we know it needs to be, which is max minus men. You also introduced the formula with an equal sign in Excel max. We're going to open the parentheses and then we're gonna just tell that we want everything in column. A and it's smart enough to ignore the word temp. Okay. Unless I tell it to consider that minus the men. Don't protect. Close those gates open parentheses. Tell it the column again, Close the parenthesis, there's your nice little formula and pay for the range. So that's a range value. And then we're gonna go do our standard deviation value. Okay, so again, we're gonna open it up. We're going to type in our formula. But we have to tell Excel what kind of standard deviation formula we wanted to use because there are two formulas you're going to learn over time, one for population value and one for a sample value. Okay, right now we're just doing sample values so ready dot s and if you're doing this in Excel, you're doing this in some other feature, you might get two values returned and S value and a sigma value. So again you're gonna want the S values for this standard deviation. Open your parentheses, tell them the whole column that you want. Close the parentheses right Round to one Decimal. Place more than the raw data. Okay. And then think about what that number means. It's telling me most healthy humans vary from the mean By less than 1°.. Okay. But just out of curiosity, let's speak. What was the average in this data set? Excel uses the word average for what you're more precisely calling the meat. Okay. Just out of curiosity they're getting an average of 98.1. That's lower than what we think. Anyway, interesting but ranging from Um .65 below or above that so maybe 98.7 should be the max expected maximum. When does account that you have a fever. So really interesting question. All right, that's all.

Question 84 is a fairly long question, says predict on Calculate the heat transport in the human body. The core temperature of human bodies 37 degrees Celsius. However, the skin is only 34 degrees Celsius. Find the rate of heat transfer out of the body under the following assumptions. The average thickness of the tissue between the corn. The skin is 1.2 centimeters, and it's got the same thermal conductivity as water. So to do that, of course, we want the rate of heat flow, which is Q over tea, which is just equal to the thermal conductivity times. The area gets to move through times the difference in temperature divided by the length of the path it's traveling, and so they tell us most of these things for water, we can look up the thermal conductivity. It is 0.6. The area they told us is 1.4 meters square. Uh, the difference in temperature from the core to the skin is three and his negative three s. Oh, the heat is leaking out. I don't have to worry about that. And then the length of the path is 1.2 centimeters which is, of course, 0.12 meters. And so we'll put all this together. Take 0.6 times, 1.4 times three Divide my 0.12 and we see that heat is flowing at a rate of 210 Jules per second. Um, now, heart be on this says without repeating the calculation of part, eh? What rate of heat transfer would I expect if the skin temperature were to fall to 31 degrees Celsius? Well, if we go from 31 our difference in temperature went from three to six, which means we're just gonna double this. So we would expect 420 Jules per second.

Okay in this question forensic scientists use this law to determine the time of the death of the accident or murder victim. Okay. And this law it is equals two T. Not plus T. One minus the note and 0.97 raised to the power T. Okay where T. D. Notes. Okay I'm writing down all the things here. First of all we're T. Note is the air temperature. Okay? Air temperature and & T. one. It is the body temperature body temperature at the time of that at the time of dead. And t. Is the temperature of the body when the body found? Okay. Body temperature when a body found. Okay so in discussion all these temperatures are given and we have we have one to know that time. T. Okay so when the death was done, death was a cult. Okay so the body was found at midnight. That is 12 o'clock midnight. Okay then when was the murder happened? Okay so We have to find out the value of small T. 1st. Okay? So the given air temperature given in the caution. That is still not. It is Their temperature is given 70° for a night. Okay. And even the body temperature at the time of death uh that we suppose it was normal condition in the normal body. So we will take 98.6 degree for a night. Okay? And when the body found it was too cool. Okay? And the temperature reduced to 80 degree for a night. Okay. All these things are given in the caution itself and now be able to find out this state. No problem. We will put the values okay, first of all use how to understand the question. Okay? And question is not hard, but understanding the question is very important. Now we will put the value. So capital City, that is temperature when body found that is 80. Because to denote that is there temperature 70 plus Stephen minus t. Not even is The body temperature at the time of their that is normal temperature 98.6- teen or dirt is 70 and 0.97 ways to the poverty. Okay, now it is simple Equation which we have to solve. Okay, so first of all, we will subtract 70 from both outside. So it will be 10 equals two 98.6 -70. That will be 28.6 And 0.97 days to the poverty. Now we will divide this 28.6 on the both outside equation. So 0.97 raised to the poverty. It will be 10 divided by 28.6. Okay, and now we will take natural algorithm in the both side of the equation. So it will be Ln 0.97 days to the poverty. It will be Ellen 10 divided by 28 six. Okay. And now we can say it will be T. L n 0.97 equals two. Ln 10 divided by 28.6. And now we will divide this in the both side of the equation. So T will be Ln 10 divided by 28.6, divided by Ln 0.97 Okay. And when we saw using the calculator, T will be Okay, approximate 30.434.5 hours. Okay. It means it means what is the meaning of this tea? Okay. When the body found, it is 34.5 hours later when the body was then when the person was killed. Okay, it is now 34.5 hours to sense the body already? Dad. Okay. So when we found the body, okay. Body found at midnight, that is 12:00 And so the body was killed. The person was killed in the name of the person is also given that is john be john doe. Okay. Was killed killed 34.5 hours before the body found. Okay, more they found and the time was that is 34 34.5 hours before the midnight. That was one day before and before one day. That was 11.30. Um That is 1.5 PM Ok. One hour 30 minutes in the noon. Okay. In the afternoon. So this will be the final and perfect answer and the explanation of the question. Thank you.

A room of temperature 70 degrees and the body's temperature is 85 degrees. One hour later, the temperature of the body is 80 degrees, assuming that at the time of death, the body's temperature was 98.6. How long has the body been dead? Okay, so this Newton's law of cooling problem and the differential equation is this. The rate of change of the temperature is proportional to the difference between the surrounding temperature and the body. Temperature to the rate of change of the temperature is proportional to the difference between the outside temperature and the body's temperature. Okay, so we know that the outside temperature or the temperature of that should not be t's of zeros hard. There should be tea syrup. T's up something. Let's call Tisa M for medium. So the temperature of the air or the temperature of the water, or whatever the body is in. So Tisa bam in this problem is 70. At the time of death, the body's temperature was 98.6, so T at time zero is 98.6. When they found the body at some time, the temperature was 85. So we don't know what time that is, so let's just call it T wan. And then an hour later, when it would be t one plus one, the temperature is 80. All right, so we need all of that so that we can This differential equation so d t d t equals k times 70 minus t so d t d t equals 70 k minus. Katie. So I'm gonna bring the k t over here so that I have ah, linear equation. So the integrating factor e to the integral k d t. Because Kay is the number in front of or the function in front of tea that gives me eats the k t. So I'm gonna multiply everything in this equation by that. Yeah. So I eat the k t d T d t Uh, Oops plus k eat the Katie t equals 70 k. Eat the Katie. Okay, so this side is the same thing as eat the k t t derivative because it's the first times the derivative of the second plus the second times, the derivative of the first. Okay, that's the trick with linear equations. Okay, so now I'm gonna integrate both sides of this with respect to little t It's on the side. I get whoops on the side. I get e to the K t. T. And on this side, I get 70 times. Okay, I'm gonna use this k for each the U D you so each the Katie, plus some constant c divide everything by you to the Katie. So you get 70 plus c e to the minus. Katie. All right. Now we know that at the time of death time zero, the body was 98.6. So 98.6 equals 70 plus c e to the zero. So 28.6 equals c. So narrow equation is t equals 70 plus 28.6 e to the minus. Katie. Then what usually happens is they give us a bit of information so we can find out what K is. But what we're gonna have to do this time is used both pieces of information to find out what K is. So 85 is 70 plus 28.6 Each of the minus K t one or 15/28 0.6 equals e to the minus. Kate Thio, someone And then the other bit of information was 80 equals 70 plus 28.6 e to the minus K times t one plus one Okay. Or 10/28 0.6 equals e to the minus. K t one times e to the minus k. Well, e to the minus. K t one is equal 15/28 10.6. So I'm gonna put that in right there. So I have 10/28 0.6 equals 15/28 0.6. Eat ra minus K. Divide this over here. So I get 10/15 equals each. The minus K or two thirds equals e to the minus K or the Ellen of two thirds equals negative K or K equals negative feelin of two thirds. All right, so now my equation is t equals, um, 70 plus 28.6 e to the Ln two thirds times teeth. Yeah. So now the question was, how long has the body been dead? Okay, so when we found it is temperature was 85 So 85 equals 70 plus 28.6 e to the l n two thirds t. So 15 of 28.6 equals E to see Ellen two thirds times T. All right, um, now I'm gonna, um I'm just gonna go and take the log of both sides, and I get Ellen at 15. Over 28.6 equals the Ellen and the eat cancel. So I get Ellen of two thirds t so t is equal to the Ellen of 15/28 0.6, divided by the Yellen of two thirds, which turns out to be 1.59 hours. There you go.


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