use-the-following-data-it-has-been-previously-established-that-for-a-certain-type-of-aa-battery-wh-8

Name: use the following data it has been previously established that for a certain type of aa battery wh 8
Uploaded: 2021-06-24
Duration: 3 min 58 s
Channel: Numerade
Description: Use the following data. It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed normally with $\mu=1.50 \mathrm{V}$ and $\sigma=0.05 \mathrm{V}$. What percent of the batteries have voltages above $1.64 \mathrm{V} ?$

Question

Use the following data. It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed normally with $\mu=1.50 \mathrm{V}$ and $\sigma=0.05 \mathrm{V}$.

What percent of the batteries have voltages above $1.64 \mathrm{V} ?$

Barsha Rana · Accepted Answer

Welcome to you Marie in the current problem we are considering the distribution of voltages of double A batteries and this voltages are distributed normally. That mean 1.50 votes and sigma 0.5 holes. Now, if we draw the normal distribution over here, that will look something like this. Okay, but this is the mean. Okay, this is the point of symmetry. Uh consider my beautiful drawing here and this is one sigma limit. This is two sigma limit and this is three sigma limit. Now the question that we are asked is what percentage of the uh written Batteries will have voltages above? 1.64, correct. So now 1.64 is again a non standard value. It&#x27;s not one sigma tau sigma three sigma limit value. So we take the process of standardization x minus mu pi sigma greater than 1.64 minus New. New is 1.50 divided by 0.05, correct. Which is equal to the probability said greater than 0.14 divided by zero 05 Date it is probability zed greater than 14 x five. So this will be said greater than 2.8. Now, what is the value of 2.8 from the tables? So if I bring the table in this will be always um so this will be always 2.8 over here, which is 0.9974. So below, if if we look at the diagram now, So we want to .8 which is 1.64. So 1.64 is going to be somewhere forward. Fear. If you consider it&#x27;s under stable, the probability of Now this stable gives probability zed less than 2.8 which is 0.9974 But we want greater than so, it will be one minus probability zero less than 2.8. That is one minus zero point 9974 Which is equal to six and then two. And then you know that you know They do 0.0026. But uh probability if we can get that 2%, it it will be 0.26% by multiplying this 100 right? There&#x27;s little .26% of the entire population. As as you can see like if you ask yourself why why is this list? Because to pointed if you see 1.64 is the value at 1.65 you get the three signal a bit. So just really a very rare value. So something more than that rare value. We have really negligible probability. That is a very negligible percent of the population will go and sit there. So only this percentage will go and sit in this area and

Jayashree Behera · Answer

So if we want the same deflection, we must have deflection initial equal toe deflections final now in section 27 point six, it is shown that the deflection off the galvanic meter needle is proportional to the product off current times magnetic field. Therefore, we can plant these two over here said we have. I thank the mission we could do. I don&#x27;t be fine Now, my good. Confused as to sense this to the rhesus proportional. Why? They&#x27;re just a little loving it. So there should be a constant factor, right? So let&#x27;s see. Ah, because of the proportionally data should be constant factor, See? But since we have both the site as the same Oh, Babel. Oh, the sea cancels off the constant or the proportionality Constant cancels out on get us too. Oh, you mean that the current and magnetic field for initial and final keys. So we have I initiative. We initially called Oh, I finally be funded. So this means that I find it should be given by I initiated times Be in your shit all much be find it So it&#x27;s plugged the values No. So yeah, 63. And that micro and feel dying&#x27;s be initial over Toby Finally, 0.8 times off the emission. So there&#x27;s two cans allowed and we&#x27;re left with 63 over 0.8. Oh, so we saw that that we get the final current Toby 78.8 micro and feel. So this is the final cutting in order. Oh, for the ah deflection off the gal. Gonna middle to be seen. So you see that if the magnetic field is decreased tau 0.8 times off, though, so isn&#x27;t eight or 86 meters check once again with the question So Okay, I I don&#x27;t find that so yes. Oh, the final answer is correct. So inject that if it&#x27;s the magnetic field decreases by 0.8 or 0.86 So, uh, whatever value or by whatever value the magnetic field is decreased, we see that the current must be increased by the same amount in orderto often the same deflection that comes from this relation

Abhishek Jana · Answer

Okay, So when whenever a circuit like this Ah, we see that there are two batteries, they&#x27;re connected and then we have three resistors. Now we always when way have to use your chops Law here because it&#x27;s a complicated circuit way have two batteries and that ketchup, ketchup slow has two sections, will start the junction rule and then we&#x27;LL do the Lupron. So when we started Junction Rule, what that tells us is first, we need to find out a junction. So, for example, we have two junctions here on let&#x27;s consider one of the junction. So for this problem, I&#x27;m taking this one as ah junction that I&#x27;m ah applying my rule Now. What this junction room tells us is if there&#x27;s a current that is going out of the junction, that should be equal to the currents, that air coming towards the junction. So we see that I do is going out and idea and I won are coming in. So that means our If we want to apply the rule, it&#x27;s going to be I too in court isto I want plus three. So that&#x27;s we found that using our intentional now we could have used this junction again because we have to consider all the junctions to use a rule. But as you can see that in this area, the eye too is coming towards the junction and then I ten. I want her going out So it&#x27;s going to give you the same expression like this so we don&#x27;t need to do this for, for this example where there might be other examples where we might need to use all the junctions. Ah, okay, so now we&#x27;LL use the loops rule. So far, lucre. What we know is, if there&#x27;s a potential drop, then there were negative sign. And if there is a potential game, then there is a positive sign. So that&#x27;s one thing to remember and the other one that we should remember or which will simply their problem is if we consider the direction off our loop. So let&#x27;s consider this look and let&#x27;s stay clockwise direction as our direction. So if the current goes with the direction that we specified, then there there&#x27;s been a negative sign, and if that goes against our if the current goes against our specified direction that there&#x27;s a positive sign. So ah two ways to remember. First of all, if we say that there&#x27;s a potential drop, so as you can see that in this very we have negative to positive. So that means there&#x27;s a potential gains. So, um, Ian, if will be positive, then here there&#x27;s a potential drop. And also since I won is going with the loop. So that&#x27;s a negative. And then I do is also going with the loot. So that&#x27;s a negative again. It&#x27;s going to be I do are two we calls to zero, and this whole thing should be equal to zero. So we got desiccation using loop rule, so we applied it on Loop one. So let&#x27;s call this Loop one, and let&#x27;s call this look too similarly if we set the direction as anti clockwise, we see that the direction that we specified is consistent with the direction of the current. So again, Artie, I d will be negative and I who are you with the natives? But then, since there&#x27;s a potential gain because it&#x27;s negative to positive, so this guy will be positive and this will be eye to no one. Okay, so that means Teo in minus I&#x27;d artery minus. I too are too is equal to zero. So? So we applied Lope rule two seconds. Now let&#x27;s see what&#x27;s given here. So we know all the resisters. We know that internal instance Now we don&#x27;t need it for the first part we need it for the second part. So we&#x27;LL come to that then we have the image Eso this one has nine bowls and this one has twelve volts. Okay, so now we have three questions and we need to find out the current. So since we have three unknown so we&#x27;ll be able to solve this. So I&#x27;ve already written down how to do it and s o that I don&#x27;t bore you s So what we did here is we wrote I&#x27;d won in terms of I to a nightie. And then we have this equations. So we planting all the values off. So we plugged in the value of our one and our two And then we plugged in the value ofthe the IMF and we substituted I won from this expression. So we took I won from this expression. Put it here on DA. That gave us this. So now we have an equation ofthe eye to an eye tree only. And from here, since this equation has a to n igh t only we wrote I too in terms ofthe tree and we substituted thiss in here. So we substituted. I do here and that on ly gave on Lee had one unknown and if we solve for it, we got the value ofthe tree now, since we know it tree, What we did is we put that back in this equation and that gave us the value ofthe eye too. Now, once we know I do and I&#x27;m tree, we plug these two guys back in this equation to find out I want on. That&#x27;s what we got as I want. All right, so now it&#x27;s all for eye. One eye to an eye tree on Now let&#x27;s goto part b and see what thing is we have to make now? The problem tells us that way. Now have internal resistance tow these am a weather. Now, since the internal residence is in serious connection with let&#x27;s ah, let&#x27;s if we consider this looks so the Internet recent is in serious connection with our one and arto and for this case, internal resistance is in serious connection with arson are too. So we can add the internal resistance it with one off the resistors and that we can do the same thing because for serious connection, we know that the resistance um Adlai nearly So if we have an internal resistance that&#x27;s around here, we can add that with our one and then we&#x27;ll just have an increase off our one And then if we do the same thing for this loop, we just add our internal resistance to our three. So we&#x27;ll just have an increasing alti and then the loop remains the same as part, eh? So we can carry forward the same calculation and we can solve for I when I do a nice tree. So that&#x27;s what I did hear What I did was I added Internal reasons are So let me write that down here. So what I did was I added the internal resistance wit. Our given are one and that gave us our new are one. And for Artie we did the same thing. We added our internal instance too rc, and that gave us our new resistance. And then we can we did the same calculation. But instead of twenty five and thirty five, we put twenty six and thirty six and then we solve it on DH. If we do that, we again get our I want I do, and I treat. So you should check. You should do the calculation and check if you&#x27;re getting the same answer as me or not. Thank you.

Kayla Gephart · Answer

So here we&#x27;re looking for the voltage across the resistor R on top of this diagram. And so here I have the diagram from the problem. And I also have drawn in the current, um, these are gonna be the directions of the current in this problem. We know that currents leave the positive ends of batteries and go into the negative ends of batteries. And so this is the only way that makes sense for the currents to flow with that rule in mind. So the way we&#x27;re going to solve this is we&#x27;re first going to find I three or the current going through the resistor we&#x27;re looking at, and then we&#x27;ll use that to find the voltage. So first, we&#x27;re going to use the junction rule at this junction here. The current going into the junction is I one plus I to, and that&#x27;s equal to the current going out of the junction, which is hi three and next. We&#x27;re going to do the loop rule on this big loop here, So starting with a battery, we have e m F one. But then we have an internal resistance, so we have to subtract I one times little are and then we&#x27;ll subtract the voltage drop from the resistor r. That&#x27;s going to be I three times big are And that brings us back to the battery, completing the loop and stats equal to zero. And then we&#x27;re going to do the same thing, the loop rule. But with this loop. So starting with battery, too, we have e m f to minus the voltage drop from the internal resistance, which is I two times are minus the voltage drop from the big resistor. I three times big are which equals zero. Now, this could be solved in a lot of different ways. Um, I&#x27;m going to skip that step, but the only thing we care about really is what I three is equal to. And if we solve this for I three, you find the I three is equal 2.617 amps. Now we can use that to find the voltage across the resistor. Sens Voltage is equal to the current time is the resistance. We could plug in both those values. Do you find that the voltage drop across the resistor is 2.47 volts and that will be our final answer

Jayashree Behera · Answer

So as you can see, they&#x27;re three currents involved. Island, I turned. I trade. So there must be three independently questions to find these currents. So one began get by a blanket of junction rule or at this point off this point, whichever one you can choose. So this would give us I do to be equal toe. I want plus I three. So I&#x27;m applying the junction rule over here on Dhe. Let&#x27;s call that a question one. And then we can apply the loop rule. Oh, to the top Plouffe This one starting with the negative terminal off the battery on and will progress clockwise. So don&#x27;t go this way, Andi, since we&#x27;re going o negative to positive inside the battery. So the e m f should be positive. So? So we should write. Plus Ah, you won. Then we&#x27;re going along the direction off current I want. So we will have negative. I want times are once again we&#x27;re going along the direction off the current I too So we should have negative. I do art on loving the values that we have a bigot. Nine equal toe 25 I won plus 48. I did it&#x27;s called is the question. Now we can apply. Look, Jul two This, uh, the bottom loop on, we start with again the negative terminal off the battery and B let&#x27;s progress a counterclockwise now so that we&#x27;ll get an idea of how the questions will change our depending on how you go. So for that case, so we&#x27;re going off again from negative to positive or inside the batteries. So we should have plus e to Then we&#x27;re going along the direction off current year I tree, so we should have negative I three times are three on dhe at this point as well we&#x27;re going along the direction off current, so we should have negative. I do our toe on DDE if you had gone clockwise here like this. So your question will ultimately be seen except for the signs. But since you you&#x27;ll have your right inside the zero, you can say that both off the hood of those questions will be saying so. Let&#x27;s write that down. So for the case going, if you&#x27;re going clockwise on your starting with the positive don terminal off the battery, so you&#x27;re going from positive to negative inside the vacuum. So you should have negative Ito. Then you&#x27;re going opposite to the direction off current I to hear. So you should have positive I d harto again. You&#x27;re going positive to our tree. Positive to the direction off current. Uh, at, uh, this is a stone, so you should have Yes. So you&#x27;re going opposite to the direction of current. At this resistance, you should have less I three artery, and this must be equal to zero on if you multiply minus one in both sides. You get this. I&#x27;m just X extending Is the stool accepting these two and want to playing minus one on either sense. So you get this a question, which is exactly same as toe what you found by going counterclockwise. So now, plugging all the values over here you get the world equal dough 35 i three plus 48 I do on Let&#x27;s call this the question three. No. In order to solve these two equations, we can start with a cushion one. Since it&#x27;s the simplest run on Let&#x27;s solve for I won, which will be eye to minus I three on dhe. Oh, where else? We will substitute I want this expression off. I won into those questions, which have I wanted them. So that&#x27;s the question to hear. I tree does not have. I won. So we will pick a question toe solved this by putting. I won, uh, this expression off, I went over here, So let&#x27;s see what we get. Hopes. So doing that. Excuse me. So I think that we will get nine equal door 25. I won, which is? I do a minus. I three let the phone from the question one less 48 I do. On DDE. We saw this on. We get nine to the equal. Do 73 I too minus 25. I treat Lex call this question to dash because we have substituted, but this is basically questioned toe. But now, instead, off I want and I do we have I ruined country. So now we have two unknowns. I two and three and two. It questions too rash and treat. So let&#x27;s pick one of these two and Sol for one alone on. I&#x27;m gonna go of it. The bottom loop or question, which is a question tree here on da. So for I too. So let me just write it this small space. So I&#x27;m solving the situation for I too. So I&#x27;ll have to equal toe 12 minus 35 53 over 48. Now that I have, I do in terms off my G I blood that expression in two dash so I&#x27;ll get nine equal toe 73 12 times 35 i trees over 48 minus 25 by three equals two groups minus turn different fights on DDE. This will give me I three. So this is basically a question with just one unknown I tree so I can solve this equation for eye tree. This would give me cereal 10.118 to appear. Or you can say this is approximately 0.1 toe Tampere on this current is I tree and is going up blood. Uh, Indra system Artie. So let me just dragon in books on DDE. This is going This is the current flowing through our tree tree and this is going up what? At a party now again, substitute this value off. I&#x27;d re ah, in tow this equation which is actually let&#x27;s call that four. Where we have I do in terms of fight three on Now that we have, I think we can find I don&#x27;t know. So then get I I do After putting I three over here to be cedar 0.1638 ampere on this is it a 0.16 ampere took those two significant visits on This is the current that is flowing through our two and it&#x27;s going towards left. So are to London left Uh, don&#x27;t buddy Eef. Don&#x27;t worry about how you are taking your currents to be. You can say that I do Is going like this? Okay, let me just pick another color. So if you say that Oh, if you had a seemed initially that I do is going in this direction Ultimately you would have arrived at a negative value off I do on dhe current, we&#x27;re considering that to be a victim, but so negative value off arguments, the direction that you have assumed the active direction off the IDU is opposite toe. What? You are what you have assumed. So if you&#x27;re you choose to your direction to be the right, you&#x27;d get a negative. I too which means that I do is flowing through what&#x27;s left. So don&#x27;t worry about how you&#x27;re choosing your science to be. It is. I don&#x27;t know. It&#x27;ll be fine after you solve everything. No. So we have a toe and finally we can find I want. So I&#x27;ll put this seclusion. You know that the soul for I want because this one is the simplest So I want is basically I do minus I three. As we have solve years, we&#x27;re basically going backward. Once you have one unknown, we can progress backward like we got a tree from Cuba. So why? Once we have I three, they can go back to the sea, question to find item. Then we got I do from this equation. So once we have a two and I&#x27;d really can get O, we can use this to question number Consol for my mom. So we get Ivan Toby zero point single for 56 ampere, which is nearly quite a 0.4 600 to 2 significant visits on this is the current flowing through our one and is going towards right Pay more to be positive. Yeah. So Assumption was studied. The hand this is flowing. Do right. Not for Billy. We have to include the internal resistance. That&#x27;s, Ah, small art. So now the battery, even Andy, to have internal justice distance off one each on instead of going over all the calculations again. What we can do is we can, since this is just right, are here and are here. So this art is in cities with our one on the same art is also in serious with all three don&#x27;t Jews arto Toby don&#x27;t assume that are from in two or even is in cities with art, because it&#x27;s not because as it cause the current splits at these two at the assumption, which means that it&#x27;s not the same current that&#x27;s going through this m f on, that&#x27;s when through our tow, the only current oh, that is throwing through even on any other sister is our one is I want on that is through our one. So even on our one quick into the Internet resistance off even on our Renard in cities. So that&#x27;s why we can say that small art and I won an art in Siri&#x27;s On small are from Ito and our tree, our agencies. So since they are in Siri&#x27;s K valiant resistance will be basically our place. Our one over here on our this are three at Oh here. So instead of doing all the calculations all over again, we can add this internal resistance toe are one on our three on Duh. Yeah, on dhe do the same gang relations. So now we have a hard one to be our one less one. So now are you in this 6 26 on our three is 36 homes on dhe. We will rework all this process again the same day. We have to see him. Everything is the same. But you have 0 35 instead of 35. You have 36 instead off drink. If I if you have 26. So I&#x27;m not gonna do all the process again. I&#x27;m sure that you already got on idea off how to do that. So I&#x27;m just gonna write the answers. So obviously first, if you go exactly the same way you find a tree first. So I could even come out to be single point 11 So the magistrate, the expression as well so I tree will be something like 38 or were 3 26 on this vehicle on DDE. Okay, so approximately this is 0.1 gland. Feel up to two significant visits on DDE since that is positive. So this is again going through Artie and upward. Similarly, I do will be, Yeah, I eat. So I told you something like one Linus t I three over four. So this question is basically this one simplification off the seclusion. So let me just group. So you have the 36 year night, So if you take a if you factor out 12 from the numerical, we&#x27;ll have one miners. Three i three Andi. Oh, in the denominator. You&#x27;ll have four with this trail times soulless 40. So this question is basically this one. So let me just go back, and it is all of that so that you don&#x27;t get confused. Yeah. So we put this value of Phi three over here on, did it your 0.1626 and beer, which is nearly called a 0.16 emptier. And this is our two bullets left. Finally, we can find I won, Which will be I do minus I three. This this equation is on stays the same because it does not have resistance in them, so it stays the same for but he and Bobby So we get. I want to be zero point cedo for six ampules on this is too. It&#x27;s night and flows through our. So now you have all the currents, including and excluding the the internal resistance.

Abhishek Jana · Answer

Okay, so in this problem way have two batteries and then we have a speak where that&#x27;s going from the making a junction, banking to junction points over here and here. If you have blanket of slaw on the right side of the junction, we see that I won and I do our going towards the junction. And then I told her eyes coming out. So if we trying to solve for the junction room, it&#x27;s going to give us because I want us. I too that&#x27;s why we wrote, I want us. I too here. Now these are the given parameters that we have. We have internal resistance. We have the resistor that&#x27;s attached. Then we have two different image toe EMFs off the batteries. Now for the new Oprah with taking two looks. One is with the internal where which is connected to this big world. And then for the second look, we&#x27;re taking the outer wearing. So for the first part, we and for both of the loops, were choosing a direction which is conical cock ways. Now for the Luke with green Ah, arrow. It&#x27;s going to be if Salon One or E m. If which is positive and then it&#x27;s gonna be minus. I want times are because I went in the direction, are the same direction. So that&#x27;s why there&#x27;s a bullet his job. And then we have Ivan plus I two times bigger on DH again. There&#x27;s an age time because there&#x27;s a voltage drop and ah, for thie for the black are arrow are the outer loop will have Absalon to minus I two times are again because they&#x27;re in the same direction. We have a negative sign. Then it will be minus. I want us. I two times are and they&#x27;re all equal zero. So now we have three questions and three s. So now we have two equations and two unknowns because we already solved, we have already solved. I haven&#x27;t I so yeah, if he saw trying to solve for it. What we have is so what we&#x27;re doing is first to writing this equation in terms ofthe eye, too. And we plug in the values there and then what we get is an expression in terms ofthe I won, right, And we can use this expression and put this over here in place off. I too, so that we can solve for I want on DH. That&#x27;s what we did here. So in place ofthe eye, too. We plugged in this value and Ah, you see Ah, let me see if I did anything wrong there. No, I think we&#x27;re fine. Um, yeah. Um right. So if we do that and sold for I, we get a current as this. Ah, it is one point. Yeah, it is minus one point one two nine names. And then we can plug this back here to solve for I too. And that gives us one point seven to eight amps. So now we know the currents. So what we can do from here is s O we need the voltage across big r. So to do so, it&#x27;s just going to be I want Plus, I two times are because that gives us the whole Destro. So, yeah, that&#x27;s going to be this. And since we know the values we can directly plug in the numbers and sulfur, it&#x27;s going to be four olds. And then for I, when we have negative one point one two nine names and for I do we have one point seven to eight ems on DH. We solve it and get our old age drop as three point three. Two point three nine six ports. Thank you.

Problem

Use the following data. The lifetimes of a certai…

Problem 16 Easy Difficulty

Use the following data. It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed normally with $\mu=1.50 \mathrm{V}$ and $\sigma=0.05 \mathrm{V}$.

What percent of the batteries have voltages above $1.64 \mathrm{V} ?$

Answer

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Boris M.

Christine G.

Lucas E.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus