4

0.222 P= 0.2414024 The candy company that makes MEM s claims that I0% of thc MEMs it produces are grcen. Suppose tat thc candics are packaged at random; and thc sma...

Question

0.222 P= 0.2414024 The candy company that makes MEM s claims that I0% of thc MEMs it produces are grcen. Suppose tat thc candics are packaged at random; and thc small bags ontain 25 MAMS. When we randomly pick a bag of MeMs we may Assume that thts represcnts 4 simple random sample of size n 225. Suppose that in 4 randomly iclccted small bag of MAM s thcre arc 5 grccn MMt What E thc valuc ulthe standard error of?" 70.0u6; 700794(uR0J02 Fheepudy culpi} that makes MAMH-laus that H"ot Ihc

0.222 P= 0.2414 024 The candy company that makes MEM s claims that I0% of thc MEMs it produces are grcen. Suppose tat thc candics are packaged at random; and thc small bags ontain 25 MAMS. When we randomly pick a bag of MeMs we may Assume that thts represcnts 4 simple random sample of size n 225. Suppose that in 4 randomly iclccted small bag of MAM s thcre arc 5 grccn MMt What E thc valuc ulthe standard error of?" 70.0u6; 700794 (uR 0J 02 Fheepudy culpi} that makes MAMH-laus that H"ot Ihc MAMS # tut ths chtdica Ie puckozed A1 randonx And l predic eart Krern Suppog muul pic bupofMMs We SnEIhp contain Ma a ebnah elz amplc fal a::mMc I: Vai Ien 4 ATren hr



Answers

The Food and Drug Administration sets Food Defect Action Levels (FDALs) for some of the various foreign substances that inevitably end up in the food we eat and liquids we drink. For example, the FDAL for insect filth in peanut butter is 3 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A random sample of 50 ten-gram portions of peanut butter is obtained and results in a sample mean of $\bar{x}=3.6$ insect fragments per ten-gram portion. (a) Why is the sampling distribution of $\bar{x}$ approximately normal? (b) What is the mean and standard deviation of the sampling distribution of $\bar{x}$ assuming $\mu=3$ and $\sigma=\sqrt{3}$ (c) Suppose a simple random sample of $n=50$ ten-gram samples of peanut butter results in a sample mean of 3.6 insect fragments. What is the probability a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments? Is this result unusual? What might we conclude?

In this question, we're told that the Food and Drug Administration sets up Some levels for the food we eat and drink. So the level for insect fault is three fragments per 10 g. And we're told we have a random sample of 5010 grand portions, which has a sample mean of 3.6. And were asked why the sampling distribution of the sample mean is approximately normal. So the reason is because we have a large enough sample size which is more than 30. So according to the central in the middle theorem, the snap cleaning distribution well X is approximately normal because we have a large enough sample size part fever asked what is the mean? And the standard deviation of the sampling distribution Of X, assuming that the population means three. So sampling distribution means three. The standard deviation of the sampling distribution effects is basically three over our sample size which is square 15, Which is 0.245. So we have our mean and standard deviation of the sampling distribution now in part C, whereas what is the probability that a simple random sample results in a mean of at least 3.6 Insect fragments. So that's probability disease more than or equal to 3.6 -3 over our standard deviation which is .245. So that is the same as one minus probably TZ less than 2.45, Which is 0.0071. So this is the probability is this result unusual. Yes, it is unusual because the probability is so low. And so what we might conclude is basically that this comes from a population with the mean actually higher than three. So it is unusual and probably comes from a different population.

Okay. So this problem we got insects and chocolate bars are average is going to be 14.4 and a 225 chocolate bar. 225g. And we're looking what is the probability that we find? zero insects in a 225 grand bar. So that's gonna be the probability that X. Is equal to zero. Yeah. And our average is gonna be 14.4 since we're looking at the whole bar And it's gonna be our -144. Uh Well it's hard to write. Mhm. Okay. And then we'll we'll divide that by one. Of course this is gonna be one. So this will be our answer. Oh but wait there's one thing I forgot here access supposed to be zero. So this part zero which makes this one. So our answer is just gonna be eating the power of negative 14.4. Next for B we have 1/5 of the bar tested. So that's gonna be your same answer from last time. Since we're looking at the probability of X equals zero. But at a different average. So it's gonna be e to the power of negative 14.4 times 0.2 for that 1/5. And that's gonna be your answer for beat. Now for seat were asked was a probability that we get at least one in a 28.35 grand bar. So first things first probability of X is at least one Is going to be equal to the probability of 1- the probability that there's zero. Yeah. Sure. I should write x equals zero. Mm. Mhm. So then we'll do that. It's gonna be one Either power of native 14 4 Times 20%. No it's not 20. It's a different percentage this time. And that's gonna be 28 0.35 Out of the 225g times are 14.4 average. And there it is. So we're going to have that be our answer On 1914.4 times 28.35 over 2 25. The power of eight. We're gonna subject one for that. And now for part D. We have. So the standard deviation is just gonna be the square roots that I mean, Which is gonna be the square root of 14.4, which is gonna be about three years old. And we're looking at more than twice. So that's gonna be like 28th and Between 14 and 28. There's not a difference of three. So, yes, this is unusual.

So in this problem, we're working with data from 50 Eminem's and they were weighed. And you need to start by finding the sample standard deviation. So we're trying to find s sub X. So I took it upon myself to put it into my calculator. I went into this stat feature of the calculator edit. And as you can see, I have the 50 pieces of data already in the calculator. So in order to find the standard deviation, we're going to hit Stat, we're gonna move over to the calculate menu and the one variable statistics. We're going to tell the calculator that we stored all of our data into list one. So in doing so, we find that our sample standard deviation is approximately 0.36 Part B. Part B is asking you to decide from a previous exercise whether the empirical rule is appropriate here. So you might not have access to that previous exercise right off the bat. But I'm gonna go back to my calculator and I'm going to look at the graph of it. So I have already put it in, and I've told it to give me a hist a gram. And when I hit graph, this is the shape you're getting, and that shape is what we would refer to as its bell shaped. So we could say, based on the history Graham from a previous exercise, it would be appropriate to use the empirical rule because the data is bell shaped. Another thing we could say is the distribution of data is approximately normal, right? So now let's go to Part C, which is asking us to actually use that empirical rule. Now, before we can use it, I think we should probably review what it says. So we're going to draw a bell shaped curve. And when you draw that bell shaped curve, we always put the average in the center, and then we count by standard deviations in each direction. And if we count one standard deviation in each direction, so that be that we're at Mu plus sigma and mu minus sigma, then you can be pretty assured that approximately 68% of your data is going to fall in there. So because the bell is symmetric in nature, if we take that 68 divide it in half, then each of these pieces would account for 34% of the data, and you can display it as either 34% or as its decimal equivalent. Now if we go two standard deviations out in each direction, so that means we're out mu plus two Sigma and U minus two Sigma. Then you could be confident that 95% of the data falls between these two values. So if you take away the 68% we've already accounted for, that means there's 27% left over meaning then that there's 13.5% in this little portion and 13.5% in this little proportion. They're a little portion then, if we go out one mawr standard deviation. So if we go out to mu plus three Sigma and Mu minus three sigma, then you are almost guaranteed to have 99.7% of the data to fall between those two numbers. And again, if you take that 99.7 and you subtract the 95% that we have already accounted for, that's going to leave you with 4.7%. And when I split that evenly into two pieces. Then this section here is going to have 20.235 And this section right here would be 0.235 And keep in mind, the entire bell is 100%. So there are little pieces beyond here that's still available. Um, and the entire bell would be that 100%. So now that we have reviewed that, let's look at the bell curve in terms of the data that we have. So we have the bell shaped data and we saw that by using the graphing calculator and in the center, we're going to put the average. And in the hint in this problem, they've already told us that the average was 0.875 And in the first step of this problem, we found that the standard deviation and actually the standard deviation should be an s rather than a sigma was 0.36 So if I add 0.362 that average, I will be at 0.911 And if I add 0.36 again, I will be at 0.947 And if I go back to that average and I subtract 0.36 I would be at 0.839 and if I subtract again, I would be at 0.803 So, in essence, I am asking you what part of the curve or what percentage of the curve would fall in between those two values. So if I look back, I'm going to standard deviations to the left and two standard deviations to the right. So that means I would expect 95% of the Eminem's in our sample to fall between these two values and the two values again, our 803 grams and 0.947 g. All right, let's talk about Part D. Part D is asking you what is the actual percentage of Eminem's that way between those two values? So whenever we're trying to find a percentage, the the easiest thing to do is to think in terms of parts and whole, and when it comes time to the whole in percentages, that would be 100% When it comes time to talking about the whole with regard to our data, all 50 would be the whole data set, and we've got to figure out how many of those 50 are between these two values. So if we go back to our calculator and I get back into my data set, I've got them in list one, but they're not in order. So it's not really easy to tell how many are between those two values. So I'm going to go back to stat, and I'm going to tell it to sort the list. So we're going to sort list one so that I could now look at the list and I can see that 0.79 is not in between 0.803 and 0.947 But then when I get to the second data point, it is. And as I keep scrolling down, the last one is not in this range. So really, there's two pieces of data that do not fall in this range, meaning that there are 48 pieces of data that do, and I need to know what part of the 100% that would represent. So if I were to cross multiply here, I would find out that the actual percentage is 96%. So the empirical rule told us 95%. Our actual data is 96%. Let's look at part E. Part E is asking us to use the empirical rule again, but this time to tell us how much is in between the values of 0.803 No, sorry is more than 0.911 g, so we want more than 0.911 So I'm going to reproduce my bell and again. At the center was 0.875 And when we went one standard deviation over, we got that 10.911 When we went to standard deviations over, we were at 0.947 and when we went to the left, we were at 0.839 and to the left one more time. Put us that 10.803 and this time we're trying to determine the percentage based on the empirical rule that would be greater than 0.911 Keeping in mind that the whole bell is 100% we're going to take away half the bell because half the bell does not meet the criteria. So we'll deduct that 50% and then we're going to take away this little section here, which accounted for 34%. So the part that is shaded the part that is greater than 0.911 is going to end up being 16% of the data should weigh more than 0.911 Gramps. And for part F, it wants to know what's the actual percentage of Eminem's that way more than the 0.911 So we're going to do like we did in part D. So for part F, we're going again. Think in terms of parts and whole in terms of percentage, the whole is 100. In terms of our data, 50 pieces of data would be the whole set of data. We're trying to figure out what part of the 100 and we're now going to look at our data, and we're going to see how many pieces of data arm or than this 0.911 So again, I'm gonna bring in my data that's already been sorted and bigger than 911 is going to be the 0.9 to the 0.9 threes. The 0.94 point 95 So we're gonna have 123456 pieces of data so we could put a six in here. And if we were to cross multiply 50 X equals 600. So therefore our actual is going to be 12, so we could say 12% of the data is actually mawr than the 0.911 g. So the empirical rule told us that 16% of the data should weigh more than and we came up with our actual data to be 12%. So, as you can see, the empirical rule is a framework. It's not perfect. It's giving you an approximate percentage off values in between certain locations on that bell curve.


Similar Solved Questions

5 answers
Which of the following graphs represents an even function?
Which of the following graphs represents an even function?...
5 answers
Consider the basis E B = {(4,1).(-1,0)} for R?, Find [w]r for w = (2,7)Find w for [wlu = (-2,11).
Consider the basis E B = {(4,1).(-1,0)} for R?, Find [w]r for w = (2,7) Find w for [wlu = (-2,11)....
5 answers
Given the portion of the circle r? + y? the first quadrant set up BUT DO NOT EVALUATE the integrals that represent the followingThe length the curve as function of xThe length of the curve as function ofy.The surface area generated by rotating the curve about the y-axis expressing the integrand as function ofy:The surface area generated by rotating the curve about the y-axis expressing the integrand as function of x
Given the portion of the circle r? + y? the first quadrant set up BUT DO NOT EVALUATE the integrals that represent the following The length the curve as function of x The length of the curve as function ofy. The surface area generated by rotating the curve about the y-axis expressing the integrand a...
5 answers
Complete the table and investigate the limit (x + 3)approaches from the leftapproaches from the right0.996,9947,0017,01{(X)
Complete the table and investigate the limit (x + 3) approaches from the left approaches from the right 0.99 6,994 7,001 7,01 {(X)...
5 answers
TBol deQuestion Find the solulion to Ihe followirig Initial value problem: y" Vz"F2v where u(0) =u(a:)Vi" +2)y(t)05("v2+2)u(a)Vz" +2 y(c)V5(VI 11Find general solution for the following differential equation:Question Type here to search
tBol de Question Find the solulion to Ihe followirig Initial value problem: y" Vz"F2v where u(0) = u(a:) Vi" +2) y(t) 05( "v2+2) u(a) Vz" +2 y(c) V5( VI 11 Find general solution for the following differential equation: Question Type here to search...
5 answers
Point) Find the general solution to y' 6y 34y = 0. Give your answer as y =?. In your answer; use €1 and €z to denote arbitrary constants and the independent variable: Enter C1 c1" and C2 ashelp (equations)
point) Find the general solution to y' 6y 34y = 0. Give your answer as y =?. In your answer; use €1 and €z to denote arbitrary constants and the independent variable: Enter C1 c1" and C2 as help (equations)...
5 answers
Determine the equation of the trend Iine through the following cost data_ Use the equation of the line to forecast cost for vearYearCost ($ million)Cost for year 7million_
Determine the equation of the trend Iine through the following cost data_ Use the equation of the line to forecast cost for vear Year Cost ($ million) Cost for year 7 million_...
5 answers
I(sy) =%' YX' (clog $ aclelle)
I(sy) =%' YX' (clog $ aclelle)...
5 answers
Convert benzene into each compound. You may also use any inorganic reagents and organic alcohols having three carbons or fewer. One step of the synthesis must use a Grignard reagent.
Convert benzene into each compound. You may also use any inorganic reagents and organic alcohols having three carbons or fewer. One step of the synthesis must use a Grignard reagent....
1 answers
The two wattmeters in Fig. 11.20 can be used to compute the total reactive power of the load. a) Prove this statement by showing that $\sqrt{3}\left(W_{2}-W_{1}\right)=\sqrt{3} V_{1} I_{L} \sin \theta_{\phi}$ b) Compute the total reactive power from the wattmeter readings for each of the loads in Example $11.6 .$ Check your computations by calculating the total reactive power directly from the given voltage and impedance.
The two wattmeters in Fig. 11.20 can be used to compute the total reactive power of the load. a) Prove this statement by showing that $\sqrt{3}\left(W_{2}-W_{1}\right)=\sqrt{3} V_{1} I_{L} \sin \theta_{\phi}$ b) Compute the total reactive power from the wattmeter readings for each of the loads in Ex...
5 answers
Variant b) Through the use of a mechanism, explain the observed product Include any mechanisms for the formation of reagents Be sure to explain any selectivity observedNaOMeCHCIa
Variant b) Through the use of a mechanism, explain the observed product Include any mechanisms for the formation of reagents Be sure to explain any selectivity observed NaOMe CHCIa...
5 answers
For each polynomial function given: (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each $x$ -intercept; (c) find the $y$ -intercept and a few points on the graph; (d) determine the end behavior; and (e) sketch the graph.$$f(x)=7 x^{5}-14 x^{4}-21 x^{3}$$
For each polynomial function given: (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each $x$ -intercept; (c) find the $y$ -intercept and a few points on the graph; (d) determine the end behavior; and (e) sketch the graph. $$f(x)=7 x^{5}-14 x^{4}-21...
5 answers
2pcProblem 4A light triangular plate OAB is in & horizontal plane: Three forces, F1 = 6.0 N; Fz = 9.0 N, and F3 = 7.0 N, act on the plate, which is pivoted about a vertical axes through point O. In the figure; F2 is perpendicular to OB. Consider the counterclockwise sense as positive. Find the sum of the torques about the vertical axis through point O, acting on the plate due to forces FL, F2,and F3.308A1.00 m0.60 mtF 2450 O0.80 mBF3
2pc Problem 4 A light triangular plate OAB is in & horizontal plane: Three forces, F1 = 6.0 N; Fz = 9.0 N, and F3 = 7.0 N, act on the plate, which is pivoted about a vertical axes through point O. In the figure; F2 is perpendicular to OB. Consider the counterclockwise sense as positive. Find the...
5 answers
Suppose that a ship’s engine survival probability is p. During voyages a ship can have upto5 engines inside it. As long as at least 1 stays operational the ship can complete its voyages.For what values of p a 3 engine ship will be more preferable to a 5 engine one?b. Explain binomial random variable.Please solve it asap. I will rate it
Suppose that a ship’s engine survival probability is p. During voyages a ship can have upto 5 engines inside it. As long as at least 1 stays operational the ship can complete its voyages. For what values of p a 3 engine ship will be more preferable to a 5 engine one? b. Explain binomial rando...
5 answers
Calculate the approximation 𝑀4 for the given function andinterval. 𝑓(𝑥)=3−𝑥,[1,3] (Use decimal notation. Give your answer tosix decimal places.) 𝑀4≈
Calculate the approximation 𝑀4 for the given function and interval. 𝑓(𝑥)=3−𝑥,[1,3] (Use decimal notation. Give your answer to six decimal places.) 𝑀4≈...
5 answers
A 0.74 kg disk and a 0.755 kg ring, both 0.12 m in diameter, arerolling along a horizontal surface at 1.4 m/s when they encounter aramp. To what height about the ground does each travel beforerolling back down?A) DiskB) RingThank you!
A 0.74 kg disk and a 0.755 kg ring, both 0.12 m in diameter, are rolling along a horizontal surface at 1.4 m/s when they encounter a ramp. To what height about the ground does each travel before rolling back down? A) Disk B) Ring Thank you!...
2 answers
Let V be a finite dimensional vector space over C and let T € L(V) . Suppose that 1 is an eigenvalue of T with multiplicity and geometric multiplicity 3 . Prove that G(A,T) = null (T _ AD)S_
Let V be a finite dimensional vector space over C and let T € L(V) . Suppose that 1 is an eigenvalue of T with multiplicity and geometric multiplicity 3 . Prove that G(A,T) = null (T _ AD)S_...
5 answers
Use a system of equations to find the partial fraction decomposition of the rational expression. Solve the system using matrices: 14x - 8 (x + 4)x - 4)2 X + 4 X -4 (x - 4)2(A, B, C)
Use a system of equations to find the partial fraction decomposition of the rational expression. Solve the system using matrices: 14x - 8 (x + 4)x - 4)2 X + 4 X -4 (x - 4)2 (A, B, C)...

-- 0.021596--