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5. A vacuum cleaner has a mean lifespan of 3.4 years, with a standard deviation of 0.4 years.Sketch a normal curve that represents the above situation showing the p...

Question

5. A vacuum cleaner has a mean lifespan of 3.4 years, with a standard deviation of 0.4 years.Sketch a normal curve that represents the above situation showing the percentage of data values that fall within 1, 2,and 3 standard deviations from the mean.6) The manufacturer stored 1400 vacuum cleaners in the storage, How many of these will serveBetween 2.6 and 3.8 years.ii_More than 3 years

5. A vacuum cleaner has a mean lifespan of 3.4 years, with a standard deviation of 0.4 years. Sketch a normal curve that represents the above situation showing the percentage of data values that fall within 1, 2,and 3 standard deviations from the mean. 6) The manufacturer stored 1400 vacuum cleaners in the storage, How many of these will serve Between 2.6 and 3.8 years. ii_ More than 3 years



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A storage battery has an expected lifetime of 4.5 years with a standard deviation of 0.5 year. Assume that the useful lives of these batteries are normally distributed. (a) Use a computer or graphing utility and Simpson's Rule (with $n=12$ ) to approximate the probability that a given battery will last for 4 to 5 years. (b) Will $10 \%$ of the batteries last less than 3 years?

All right, we are on problem number 32. The lives of refrigerators are normally distributed with me 14 years and standard deviation is 2.5 years. So it is a normal distribution. Where new is 14 means the point around which the normal distribution is symmetric. So this is 14. And what is the standard deviation? Standard deviation is 2.5 years, which means the, uh, new minus sigma and new plus Sigma. These will be the points of inflection, right? Our meal is 14 are sigma is given to assess 2.5 years. All right, so what are the points of inflection? Mu minus Sigma 14 minus 2.5, which is 11.5 late. And then you plus Sigma, which is 16.5. These are the points where the curve is going to change its curvature. All right, The first question is draw the normal curve. We've already done that. Then it says that shaped the region. That represents the proportion of refrigerators that lasts for more than 17 years for more than 17 years. Okay, so this is 16.5 now. If you draw this with the help of a statistical software. You will be able to level it. Exactly. I'm just doing this over here as a rough estimate right now. Just a moment. Yeah. Okay. So 17 is going to lie somewhere around here, right? This point is going to be 17. So the area to the right of it is what we are interested in, right? Because we want to shared the reason that represents the pope the proportion of refrigerators that last for more than 17 years. Okay, so this is the area to the right now, Part C says suppose that the area under the normal curve to the right of excessive below 17 is 170.1151 which means that this shaded region is 0.1151 This means what, 15.51% of refrigerators of referee generators last more than 17 last more than 17 years. Right. And what is another way to represent this or interpret this? What is the question saying? Provide two interpretations, right. Okay, So what will be another way to interpret this? This is or I can say that 88.49% of refrigerators of refrigerators last for less than 17 years. For less than 17 years, this will be our answer

Welcome to New married. In the current problem we are given that life of repeated refrigerators is the variable under consideration. So life of I will say fridges. It's easy and short than refrigerators. And this follows a normal distribution with new is equals two 14 years and cigna is equal in school people. Right? Yes. No. First till you got here in the last days to draw the cough. Okay. And second we have to find that the regional that is less than equal to 17 years. and the 3rd 1 is that Suppose this probability of excellence and equals 2 17 is equals two 0.1151. Then what does it mean if this. Okay bagram first itself we will get this. We're here. Okay until you do if you see The distribution has centered at 14. So this will be about 14. So So this is 14 and then 14 -2.5 with this because 14 -2.5 that will be one sick Magistrates, correct? Each of these are sigma sigma sigma. Today is minus three sigma and it is lustrous sigma plate. So this would give us 11.5. Then again if i subtract 2.5 I get nine Again if i subtract 2.5 I get 7.5. Now for 14 if I add 2.5 I get 16.5 Again if I had 2.5 I will get Yeah. Uh huh 19 If I again add I will get 21.5. Now If you see 1717 will lie somewhere over here. Got it. So we had 17 over here. So therefore in this peace if you see what is the probability at it is more than 17 years. So of course this should not be the sign. It should be greater than equal to that is the right side of the distribution. So this is the media that is she did. Okay. This is part of are A. Is this diagram. And of course in the diagram you don't have to show this. Yes, everything you should show. So this is a diagram. B. And now part B. Part beast. Part C. Is telling. Okay, if this this probability is 0.1151, What do you interpret out of it? So for interpretation, what we can do is we can utilize this case to write the interpretation. So the first interpretation is refrigerators exceeding 17 years of life is uh quite rare phenomena, right? Because as out of 100% only 102 0.1151. The physicals to 11.51 experiences product only out of only experiences that long. Yeah, lifetime. Okay, So it can be thought like somebody using it with too much of care and responsibility. Only those people will be able to have or maybe the machine will be so good that it will be going beyond 17 years. And what is other interpretation? The second interpretation? The second interpretation is the fridge is the refrigerators are expected to the fridge? Is us expected to function still 17 years As 100 -11.51 percent. So how much will that be? Nine four eight. Eat. Okay, so 88%, That is near about 90% writes. The majority of the population is below This. So they are expected to have a like a maximum teen 17 years. So from this one number we can look at the entire dark uh data set from two point of view, one is greater than one is the less than okay. What if the less than values what if the greater than values. So I hope you're able to understand this. Let me know if you have any questions

Welcome to new Madrid. In the current problem we are given to observe the uh, light time of tires with the normal distribution. Then the current question they asked that the manufacturer guarantees that if the tires do not last at least 75,000 kilometers, Okay, that is if X does not exceed 75,000, Yes, Okay, they will replace, Okay, they will be replaced and then this guarantee, so we have to find them what percent of the tires may be needed to do that. Okay, so that means what what person, if it is exceeds this, then it is fine. But if it does not accept then they have to reduce. So we need to know this percentage. Right? So let's go and check. So it will be probability of x minus mu by sigma, less than 75,000 minus mu by sigma. Which will be probability of said less than now 75 minus 100. So it is minus 25 1000 by 10,000. Right, So that will be probability of zero, less than minus 2.5. Now think of a standard normal distribution, this goes from minus three to plus three, correct? So minus 2.5 is pretty much a rear value. Right? So there should be very thin chance of this. Let us verify. Let us bring the normal table over here and check. So now if you see 2.5 over here, give this 1 to 0.99 38 correct? So this value will be because the probability of said greater than 2.5. Right? That will be one minus probability of then or less than 2.5 mm That is we will have two and this will be force of six and then zero. You know, So that means 0.62 Or in terms of percentage it will be a 0.62% of the total sample Should be uh, X cd. Yeah. Uh, sorry. Should be should not shouldn't be getting there. That is out of this entire Okay, only 0.62 That is 0.62 It's merely 1%. So 1% of the data, mainly the replacement by the manufacturer. So 0.62% of users of tires will required uh huh replacement under the guarantee. So I hope you could understand this. Let me know if you have any questions.

Into this lesson in this lesson, we have the likelihood of a number that is less than the mean or in a certain range. And that has given us the E to the power negative. Me and my standard deviation man is a mean squared divided by two types. Standard revision squared All of us on innovation I squared of two back. So the mean is giving us we're giving cowan 100,000 as the mean. Then 10,000 as the standard deviation. The pie has a regular value three A Constant Value 3.14159. No. Yeah. Yeah. So making the substitution in order to find the likelihood. So E. That would have Mhm squared Oliver too squared then All over. Okay, so this is equal to 0.000039. So this is Go in 12 Still zero Part 0. There were 39%. All right. So this is the likelihood. That's value is less than 98,200. All right. So times for a time this is the end of the lesson. Yeah.


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