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The Precision Scientific Instrument Company manulaclures thermomelers that are supposed give readings of 08€ at Ihe freezing point of water: Tests on large sa...

Question

The Precision Scientific Instrument Company manulaclures thermomelers that are supposed give readings of 08€ at Ihe freezing point of water: Tests on large sample of these tnermomelers revea that at the freezing point of water; some give readings below 0?C (denoted by negative numbers) and some give readings above C (denoted by posilive numbers) Assume that the mean reading C and the standard devialion of the readings 00"c Also assume thal Ihe frequency distribution of errors closel resem

The Precision Scientific Instrument Company manulaclures thermomelers that are supposed give readings of 08€ at Ihe freezing point of water: Tests on large sample of these tnermomelers revea that at the freezing point of water; some give readings below 0?C (denoted by negative numbers) and some give readings above C (denoted by posilive numbers) Assume that the mean reading C and the standard devialion of the readings 00"c Also assume thal Ihe frequency distribution of errors closel resembles Ihe normal distribution . Ihermometer is randomly ected and tested_ quality control analyst wants examine thermometers that give readings in the bollom 4%. Find the temperature reading that separates the boltom 4% from the others_ Round two decimal places: 63? 1.48" 89? 1.75" 0c:



Answers

Two thermocouples (temperature measurement devices) are tested by inserting their probes in boiling water, recording the readings, removing and drying the probes, and then doing it again. The results of five measurements are as follows:
(a) For each set of temperature readings, calculate the sample mean, the range, and the sample standard deviation. (b) Which thermocouple readings exhibit the higher degree of scatter? Which thermocouple is more accurate? Explain your answers.

Hi. So today we'll be going over. Mr. Arness is cabin s O. She lives in Colorado. The thermostats she sets the thermostat, the 50 F 50 F. Right here. 50 F. Okay. And then the fat thumb The fat oven table shows a distribution that looks like that. And in this case, the graph kind of shifts towards the right. Right? There's more on the left side. Right? There's more on the left side, but it trails. It gets skin year. Put the right. And so if you can imagine if you place the skier if you place the skier, scare always goes down. And so, if you place a skier at the top of the hill right here placed our little skier right here, right? Which way would the skier go down? And in this case, to go to the right. And so this distribution is right. Skewed. Right. That's what we call a rights. You'd distribution. Um, another case if it kind of if it resembles the shape like this. If you put you're skier on here, right here, then this year to go to the left. And so this is left skewed came now let's go. It's the second point. So the manufacturer claims that one standard deviation is 3 F. Manufacturer claims that the standard deviations 3 F when you look at what's given to you in the problem and says that the variance from the actual sample so the S squared X is equal to 25 and variants very answer year variants s squared X is equal to the standard deviation squared. And so if you take 25 right, you want to get the standard deviation of the rial. They're the thermostat, and so you'll take 25 plus the square Dax. And in this equation that is equal to standard deviation squared. So let's see him. If you want to get just just standard deviation alone, just want to get it alone. You have to square root this you square both sides and you actually see that their thermostat ah is actually the standard deviation. Actually, five. And so the manufacturers claim of the thermostat being on Lee. Three degrees went right. One standard deviation three degrees is actually false. This one is the rial. Ah, manufacturer. Yeah, the pen doesn't work. This is the rial manufacturer. Ah, number here. And so in this case, we can see that the manufacturer was actually false, right? His claim was false or their claim was false. And so, if this for example, the variance was lower than in this case, nine right? If the variance was lower than nine is lower than nine. If if it was nine, then once the interview Shin will be three. And so in this case, the claim will be true. And so for the manufacturers claim to be right, the variance that ms uh, what's the starkness? Should have got an should have been e less than or equal to nine. And so since it was greater right here since I was a greater we see at the manufacturers claim appears to be false.

And this example will be looking at a rectangular distribution, also called continuous uniform distribution. This is the situation where we're looking at a rectangle formed on a closed interval alpha beta with the selection inside there on a closed interval A and B. And our formula for the probability that X lies between A and B is B minus A, divided by B minus alpha. And in our particular problem, alpha and beta are determined to be -0.05 And 0.05. So in the first part, I want to know the probability that X is less than or equal to 0.03 microseconds. All right. So it can't get any smaller than negative 0.05. So that means they will be -0.05 and B will be the larger value. Now, I'm going to plug the information into my formula. So B minus a, divided by beta minus alpha. And the next example, I want to know the probability that I might have Oh more than so. It's not equal to just more than And recall my area can't get any bigger than beta. So that means in this case a will be negative 0.02 and be Will be 0.05. And to find that probability B minus a divided by peter minus alpha. And then I do the calculations. Then there you go. For C. I'm actually looking at a situation where I want to know the probability that X will be between These two, values of 0- .04 and .01. So that means they will be -0.04 and B will be 0.01. Again, just a matter of plugging the values in B minus A divided by beta minus alpha. And then lastly, I mask defying the mean and the standard deviation. So our formula to find the mean is alpha plus beta divided by two. So in our example negative 0.5 plus 0.5 divided by two. The numerator is zero Which means the mean is zero. And then our standard deviation formula is beta minus alpha, divided by the square root of 12. So that would be 0.05 -0.05, Divided by Radical 12. Mhm. And that's approximately 0.289. And then we need to were asked if our measurements are unbiased and in fact we can be sure that they are because We have a mean of zero and that would indicate that our information, our measurements are actually unbiased. I'm sorry, I ran out of room.

And this example will be looking at a rectangular distribution, also called continuous uniform distribution. This is the situation where we're looking at a rectangle formed on a closed interval alpha beta with the selection inside there on a closed interval A and B. And our formula for the probability that X lies between A and B is B minus A, divided by B minus alpha. And in our particular problem, alpha and beta are determined to be -0.05 And 0.05. So in the first part, I want to know the probability that X is less than or equal to 0.03 microseconds. All right. So it can't get any smaller than negative 0.05. So that means they will be -0.05 and B will be the larger value. Now, I'm going to plug the information into my formula. So B minus a, divided by beta minus alpha. And the next example, I want to know the probability that I might have Oh more than so. It's not equal to just more than And recall my area can't get any bigger than beta. So that means in this case a will be negative 0.02 and be Will be 0.05. And to find that probability B minus a divided by peter minus alpha. And then I do the calculations. Then there you go. For C. I'm actually looking at a situation where I want to know the probability that X will be between These two, values of 0- .04 and .01. So that means they will be -0.04 and B will be 0.01. Again, just a matter of plugging the values in B minus A divided by beta minus alpha. And then lastly, I mask defying the mean and the standard deviation. So our formula to find the mean is alpha plus beta divided by two. So in our example negative 0.5 plus 0.5 divided by two. The numerator is zero, Which means the mean is zero. And then our standard deviation formula is beta minus alpha, divided by the square root of 12. So that would be 0.05 -0.05, Divided by Radical 12. Mhm. And that's approximately 0.289. And then we need to were asked if our measurements are unbiased and in fact we can be sure that they are because We have a mean of zero and that would indicate that our information, our measurements are actually unbiased. I'm sorry, I ran out of room.


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