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Question

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Answers

The actual volumes of quart-size jars of Hellmann's mayonnaise are uniformly distributed from 31.51 to 32.46 fluid ounces. Find the average volume of a quart-size jar of Hellmann's (in fluid ounces). NOTE: There are 32 fluid ounces in a quart.
A) 31.985
B) 32.014
C) 31.890
D) 31.957
E) 32.080
F) 31.919
G) 32.052

Solving party of this problem. So first I will write all the given data. It is given edge point the toe by. This is too And K. is three. So I can write develop cube Born. Did you two fight World three is equal to three 773. But part B. The value is given edge fine. Fight 20 gauge for Q point you to fight 24 is equal to three 9 5 p. eight. No for part C. This value is given a point you to fight. This value is given age 42 and kids given us pipe. So You .05 42.5. physical to 4.0 39. So In party I can write everyone is equal to μ two is equal to mu tree is equal to mu food with And is equal to 34. So here I can write cue .0534, It's called 3.845 is the answer.

In problem 22. We want to use a graphing utility to find the mean, the variance and the standard division for this dynasty probability density function, then find the given. Probably let's start by the meat. The mean equals the integration from Italy. It seems like it's an exponential distribution which starts at zero and ends at infinity. This means the integration is from zero to infinity for X. Multiplied by F of X. Yes, we can use this moose as a graphic utility to calculate this integration. Yeah, X is defined here. The integration is represented by eight. Then we can adhere X to get new and make the limits from zero at a to infinity. That be we can see that the answer is one and third. The new equals four divided by three. The variance can be calculated using the same way the integration from zero to infinity. For X square every X the x minus mu squared. Let's get this. Using this. Must we just add a square here. Then it's a 3.5556 deployed by nine. It's 32 divided by nine equals 72 divided by nine minus 16 divided by nine. It gives 16 divided by nine. And this is the very to get the standard deviation is the square root of the variance, acquire square root of 16 divided by nine, gives four divided by three. Finally, to calculate the given probability, the probability for X to be greater than equal 0.27 we integrate the function from all boy to seven to infinity for f of X the X it's used christmas for the last time by removing excess square from here and make the limits, started to add 4.270 point 27 and goes to infinity. This gives the area this area which represents the probability 4.8167 4.8167 And this is an of the answer.

Here in discussion in part a let XB the average this stance in the well 49 lying follows uh normal distribution bit, I mean 2 50 and the standard aviation 15 that is new equal to 2 50 and sigma is quoting 50 No, yeah it is even X belongs to end of new and sigma then expert, longstreet and of well sigma do I did buy scared Rudolph and no e of expose is equal to immune is equal to 250 and sigma X is equal to sigma divided by square Rudolph and no on substitute 54 sigma and 49 for when we get sigma X is equal to 50 divided by the square root of 49 On simplifying this we get sigma X is equal to 7.142 nine. Therefore the average distance in treat for 49 fly balls follows normal between to reality and the standard deviation 7.142 nine. No, in part me from the about information, It's clear that new is equal to 250 and sigma is equal to 7.142 nine. No, I can see that be of capital channel is great. Less than Equal to small. That equal to zero mm seal. Now here From the standard normal table, the value of set that corresponds to the probability of zero it is That equal to 0.8 Yeah. Therefore uh value oh about eight years for saint tile there is of 10. Hello, that is small. That equal to expert minus. Well you I did buy sigma divided by the squared Rudolph. And now here we substitute the values two calculator Expert. Or we can say the value of the 88% time From above. We get 0.84 equal to export -250 divided by 7.1429. I'm simplifying this Big at 0.84. multiplied by 7.1429 equal to X. Were finest too. 50. Oh yeah, Expert is equal to 250 less 6.0. Or we can say extra is equal to 256. Therefore the 88%ile of the distribution of the average of 49 fly balls is 56. This is the required solution.

In this problem. Crast to analyze the volume in some mayonnaise jars. So we're told that the jars are supposed to have 32 ounces in. That's the goal. And we're told that in reality that's not the case that we have a uniform distribution between 31.51 ounces and 32.46 houses. Were then asked to find what is the average uh volume for these Hellman jars. So in order to do that, let's get a visualization for the distribution. Right? So we have zero way down over here and then somewhere over here we have crazy big numbers, right? Increasing always. Right. And we're told that we have a uniform distribution between 31.5 one and 32 0.46 So our distribution looks like this, it's zero everywhere until we're at 31.51 And then it's up here with a horizontal line from 31.51 all the way to 32.46 And after that it's zero again. And the key here is that the area underneath this curve is going to be one right. The uniform tells us that it's a uniform height, so it's the same everywhere in the area underneath. Here is one. So were then asked to find what would the average volume V. So in this case, right, we ask ourselves what does the average mean? So average means the meat. Right? The mode would be what occurs most often. Right. And so we're looking for the mean. And the visual analogue to what the mean is in this distribution is it's going to be the center of mass. So if our distribution looked different than our our center of mass might be more difficult to find. But given that this is just a uniform distribution, right, the center of mass, it's simply going to be the middle right here, Right? This is the point at which we put a uh a point to hold it, the distribution would balance itself. So how do we compute what this is? So it's exactly in the middle? So what we need to do is take 31 0.51 and add 32 0.46 And then divide by two. Right? So all we're trying to do is find the midpoint or the average of the extremes. This works because it's a uniform distribution. So all we're looking for is the middle. So it is 31.51 plus 32 point or six. Well, that is going to be 63 point 97 then we're dividing by two. And when we divide by two, we get 31 0.9 eight five. So our average weight is 31 point 985 ounces.


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