5

QUestion 14Use the one-sided Chebyshev inequality to find an upper bound for the Suppose that the chickens In a (arm produce an average 0f 31 eggs per weck with var...

Question

QUestion 14Use the one-sided Chebyshev inequality to find an upper bound for the Suppose that the chickens In a (arm produce an average 0f 31 eggs per weck with varlance ProDobeyansrehe number of egg3 produced next Week by these chickens s at least 44 TYPE YOUR ANSWER AS THE NEAREST NUMBER WITH TWO DECIMAL DIGITS:

QUestion 14 Use the one-sided Chebyshev inequality to find an upper bound for the Suppose that the chickens In a (arm produce an average 0f 31 eggs per weck with varlance ProDobeyansrehe number of egg3 produced next Week by these chickens s at least 44 TYPE YOUR ANSWER AS THE NEAREST NUMBER WITH TWO DECIMAL DIGITS:



Answers

The weights $X$ of eggs produced at a particular farm are normally distributed with mean 1.72 ounces and standard deviation 0.12 ounce. Eggs whose weights lie in the middle $75 \%$ of the distribution of weights of all eggs are classified as "medium." Find the maximum and minimum weights of such egBs. (These weights are endpoints of an interval that is symmetric about the mean and in which the weights of $75 \%$ of the eggs produced at this farm lie.)

In this question, we are asked to calculate this probability for binomial random variables for K equals two and three and then compared to the upper bound given by Chevy Chevy shelves Inequality and we're first has to do it. Assuming X is a binomial random variable based on size of 20 and a probability of success of 0.5. So we must first calculate the mean so the mean oven of ah binomial random variable is en times P just equal to 20 time 0.5, which gives us 10 and next. We need the standard deviation. Standard deviation of a binomial random variable is equal to the square root of n times P Times one minus p, and this comes out to approximately 2.24 So for cake was too. This is the probability that the distance of the number of successes from the mean being greater than or equal to two standard deviations. So now we can rewrite this equation where this probability So it's the probability that the absolute value of a number of successes minus the mean, which is 10 it's greater than or equal to two times 2.24 And now there are two ways for this to be true. We can have the probability of X minus 10. That's greater than or equal to 4.48 plus the probability that X minus 10 is less than or equal to minus 4.48 And this happens when we remove the absolute value operator. I would say that is equal to be probability that X is greater than or equal to. We add 10 to the right side we attended. Besides, so there's 10 here. Move it. Over here we get X is greater than or equal to 14.2 point 48 But because we can only have entered your values for the number of successes, we will say that X must be greater than or equal to 15. And likewise here will say that X must be less than or equal to five, which is equal to one minus probability of having, at most, 14 successes. Plus the probability of having at most five successes is equal to one minus zero point 979 plus 0.2 one, and this comes out to about 0.4 one And now for Chevy Shoves and Equality. The probability of being within two standard deviations is given by one over K squared. And here K is too. So it means the probability of being within two standard deviations is less than or equal to 1/4. Yeah, we should probably right that out first time anyway. So So, using Chevy shelves, we have the probability of being at least two standard deviations. Being at least K standard deviations away from the mean is less than or equal to one over K squared. So it's listener equity 1/4. So this is the upper bound for the estimate using Chevy shoves, and this is the actual veil value. And so now we repeat for K, it was three. So we have a probability of magnitude absolute value of X minus 10 creator than or equal to three times 2.24 So I'm basically just revisiting this here, except that I'm using three instead of two this time. And so this is equal to the probability that X is at least 17 so it would be at least 16.72 but using integers at least 17 plus the probability of getting at most three successes, and this comes out to about 0.0 26 and then using Chevy shivs inequality we have following So Chevy shelves Inequality tells us that an upper bound would be won over nine, and the true valley that we calculated was 0.26

Very in order to solve. For this problem, we can set up this inequality 118 is less than or equal to 3.14 times D, which is less than or equal to 122 to isolate for D, we can divide by 3.14 and that will make that 3.14 go away in front of our D. And we will need to do that to all sides of our inequality statement. So on the left hand side, then we would be left with 37 0.58 which is less than or equal to D, which is less than or equal to 38 0.85.

Hey, it's clear Someone new right here. So first we're gonna get the general expression for the probability. Then we know that Kay and they are both positive so we could simplify the equation. No p Oh, that's absolute value. Cranberry equal to K beta, which is equal to probability. Uh, x minus mean over a standardized standard deviation is less than or equal to negative came waas need kovacs minus mean where esty was bigger or equal to came, then standardizing it. It gives us ability that Z is less than or equal to negative K plus probability at sea is bigger or equal to King. So Z is a standard normal distribution CDF of bis e so he can reign. Probability X minus, I mean is bigger equal to que tons. Standard deviation is equal to two times one minus fly. Hey, so we're gonna use the expression from the first equation should I hear and we're going to calculate the probability for K is equal to 12 and three, respectively. So probability that minus ween, big art or he pulled too. Dana probability of x minus mean there's bigger able to to lida in probability that X minus mean, that's the value is bigger eagle everything. And then we calculate those two get to terms one minus by one, which we get two times one minus point or 13 We have a 0.3174 Let's get to minus one. Two times one minus 52 which we get two times one minus 10.9772 When we get 0.4 53 Finally you get two tons. One minus. Why? I turned 53 We got two tons. One minus 10.99 meets have been what you get? 0.26 And we know, uh, the upper limits because one smaller than one for two. No, it's less than our people. 2.2543 less than were people thio 0.1111 so we could see that the probabilities are within the upper bounds

He has a clear selling game right here. So first, we're gonna obtain the general expression for a possibility. So you got that to be X minus? I mean a bigger eagle two k time's dinner deviation, and this is equal to probability. X minus mean, it's less than or equal to k time. Standard deviation plus probability. Absolute value off X minus. Mean, this bigger or equal to K comes standard aviation Kate, and centered the reason, or both positive. So that's why you could simplify the equation as this. So we get this is equal to probability of X minus me. Perverse standard deviation is less than or equal to negative cake. Then probability perfects minus mean over 30 deviation. Course Bear Eagle's cape. And when we standardize this, you got probability, See, is less than or equal to Nick Could f K plus probability. Clancy is bigger or equal to K and Z is a standard normal distribution with CDF. I see so we can write probability that x minus mean it's bigger equal to K. S. T is equal to fi of negative king close one minus five K, which is equal to one minus five K plus one minus by the came just equal to two times one minus five K. Now we're gonna use expressions for K 12 and three, respectively. So probability about super value of X minus mean bigger, equal to center Deviation is equal to two times one minus by of one poetry get to terms one minus point 413 But you get a 0.3174 Probability that perhaps, if I u x minus meanness bigger equal to to S T is equal to two times one minus five to which we get two times one minus 10.9772 But we got 0.4 Boston It's last night for K equals three, you got absolute value of X minus mean is bigger equal to three misty jersey for 22 times one minus 53 which we get to two turns one minus 10.9 97. And this is eventually 2.26 for the upper limits for 12 and three. When we write face down, this is to SD on Mrs Points to five. These are absolute values. Three sd Standard deviation is less than point 1111 So we know that the problem is they're well within the


Similar Solved Questions

5 answers
Space capsule of mass 475 kg is at rest 8.00 x 10'/ m from the center of the Earth_ When it has fallen 3.50 x 106 m closer the Earth, find the following What is the change in the system'$ gravitational potential energy?(b) Find the speed of the satellite at that point: mfs
space capsule of mass 475 kg is at rest 8.00 x 10'/ m from the center of the Earth_ When it has fallen 3.50 x 106 m closer the Earth, find the following What is the change in the system'$ gravitational potential energy? (b) Find the speed of the satellite at that point: mfs...
5 answers
Factor completely the polynomial 6x5 + 5.4 + 20r3 + 1522 +61 + 1 _Hint:66 = (a _ b)(a + b)(a? + ab + 62)(a2 ab + 62) _
Factor completely the polynomial 6x5 + 5.4 + 20r3 + 1522 +61 + 1 _ Hint: 66 = (a _ b)(a + b)(a? + ab + 62)(a2 ab + 62) _...
5 answers
Suntanswer 43 (Write your point (2,0,3). atthe xlat parametric equations ) of fkx,y;z) - derivative Find the directional (10)x7 pts:- 2i-j + 2k. direction of v the point (4,1,1) inthe Plant tat containst8 Find te 2quatie" & (t SneAo4 P"_ Md MAA
sunt answer 43 (Write your point (2,0,3). atthe xlat parametric equations ) of fkx,y;z) - derivative Find the directional (10)x7 pts:- 2i-j + 2k. direction of v the point (4,1,1) inthe Plant tat containst8 Find te 2quatie" & (t SneAo4 P"_ Md MAA...
5 answers
Crcut d arrar) arranged $0 Ihat tho buib Ights Upoad your IJe here CR undor Ihe ioldor Drex # bultory Iwo bulbs and. sonlo iro5 (nol #Suniisson 0f Exam Wolk" afior tne examNaed nua
crcut d arrar) arranged $0 Ihat tho buib Ights Upoad your IJe here CR undor Ihe ioldor Drex # bultory Iwo bulbs and. sonlo iro5 (nol #Suniisson 0f Exam Wolk" afior tne exam Naed nua...
5 answers
7_ Calculate the average chemical formula and its range of variability for soil humic and fulvic acids using the composition data in the table presented here. Does the H-to-C molar ratio differ significantly between the two humic substances?HNSHumic substance (g kg-1) (g kg-1) (g kg-1) (g kg-1) (g kg-1) Humic acid 554+38 48 + 10 36 + 13 8 + 6 360 + 37 Fulvic acid 453 + 54 50 + 10 26 = 13 13 + 11 462 = 52
7_ Calculate the average chemical formula and its range of variability for soil humic and fulvic acids using the composition data in the table presented here. Does the H-to-C molar ratio differ significantly between the two humic substances? H N S Humic substance (g kg-1) (g kg-1) (g kg-1) (g kg-1) ...
5 answers
[} pts]: Sole thc tight trianelc ( € . fud tl: nissing sidks & Jd €, and thc analc 0 You €4a protldcyour tolutlon for tbe ao sldts and € simpllacd trigoacueari expression ior Fca: But Jou do pol netd f0 Ectuthy compute tbe Mp4l Lesw25} t0 $Lrs and € siczt 30 ckcelators 4rz aliontd Te pegk 0 CANbe computrd75oI0Q
[} pts]: Sole thc tight trianelc ( € . fud tl: nissing sidks & Jd €, and thc analc 0 You €4a protldcyour tolutlon for tbe ao sldts and € simpllacd trigoacueari expression ior Fca: But Jou do pol netd f0 Ectuthy compute tbe Mp4l Lesw25} t0 $Lrs and € siczt 30 ckcelat...
5 answers
A pattern of fringes is produced when monochromatic light passes through a pair of thin slits. Would such a patern be produced by three parallel thin slits? By thousands of such shes? Give an example to support. your answers.
A pattern of fringes is produced when monochromatic light passes through a pair of thin slits. Would such a patern be produced by three parallel thin slits? By thousands of such shes? Give an example to support. your answers....
5 answers
Assume that the power seriesan(r + 4)" converges for €9and diverges for 1 = 2.Which of the following statements about this power series must be true? Diverges for I 10_ 2. Diverges for I ~10 Converges absolutely for I 8.9 Converges absolutely for I1and only1and 3 onlyAll must be tnue1,3,and 4 only
Assume that the power series an(r + 4)" converges for € 9and diverges for 1 = 2. Which of the following statements about this power series must be true? Diverges for I 10_ 2. Diverges for I ~10 Converges absolutely for I 8.9 Converges absolutely for I 1and only 1and 3 only All must be tnu...
1 answers
Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Vertex or Vertices} \\ \text{Ellipse} &(20,0),(4, \pi)\end{array}$$
Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc} \text{Conic} & \text{Vertex or Vertices} \\ \text{Ellipse} &(20,0),(4, \pi)\end{array}$$...
5 answers
A 421-Hz whistke moved toward a Eistener Jt 4 speed 0l 19.1 MVs whzt is the npojrcnt Irequency heard by the Iistener? (T spacd of sourd 31D MijJ
A 421-Hz whistke moved toward a Eistener Jt 4 speed 0l 19.1 MVs whzt is the npojrcnt Irequency heard by the Iistener? (T spacd of sourd 31D MijJ...
5 answers
Thc Bnitish neaure body wtght by Ihe stona OCne 20 stone Ovtr {he couri of 2 Tej>Mnard0 687 exh duy t0 RiMnYejr _ 365 djvs L0lb fat 3500 kcallJan krARDo170 LEal3LI
Thc Bnitish neaure body wtght by Ihe stona OCne 20 stone Ovtr {he couri of 2 Tej> Mnard 0 687 exh duy t0 RiMn Yejr _ 365 djvs L0lb fat 3500 kcall Jan kr ARDo 170 LEal 3LI...
1 answers
Assume that there are no deposits or withdrawals. Comparison of Compounding Methods. An initial deposit of $\$ 5,000$ grows at an annual rate of $8.5 \%$ for 5 years. Compare the final balances resulting from annual compounding and continuous compounding.
Assume that there are no deposits or withdrawals. Comparison of Compounding Methods. An initial deposit of $\$ 5,000$ grows at an annual rate of $8.5 \%$ for 5 years. Compare the final balances resulting from annual compounding and continuous compounding....
5 answers
Question 13 (1 point) Refer to the electrons from below to answers are possible; if no answer the ' following question (multiple answer; then pick "none ": Which electronts) islare) spinning in a direction different from that of the others? Select = cortect answerts) 0r,1,1,+)None0(,1,0,+)0(.2-1,+)0r,2, -1,+%)0n,0,0,-%)0u,1,-1,+%)0(,1,-1,+%
Question 13 (1 point) Refer to the electrons from below to answers are possible; if no answer the ' following question (multiple answer; then pick "none ": Which electronts) islare) spinning in a direction different from that of the others? Select = cortect answerts) 0r,1,1,+) None 0(...
5 answers
{ Jh each a point in which time V V the Inodel resourceas "Woichcerxhe with H capacily variables 5Is sclzed
{ Jh each a point in which time V V the Inodel resourceas "Woichcerxhe with H capacily variables 5Is sclzed...
5 answers
Let T be the triangular area in R? with vertices {(0,0), (-1,),(1,3)}. Use the transformation 31)/4to calculate f fk+x4+-s)dxdy: (6 pts )(+nr
Let T be the triangular area in R? with vertices {(0,0), (-1,),(1,3)}. Use the transformation 31)/4to calculate f fk+x4+-s)dxdy: (6 pts ) (+nr...
5 answers
Moacrigiven Foy-echelon TormWrite the systemequations (or Wnich thc niven matrixquamenicc matrix- (Enter each jnswcrtcrnsX,Ya Z, and #.)+x+ 2y+ 32y-2Zw + 2(6) Usc back-substitutionsolvc (nc Syscem(xYr z, W)4,3 1,3
moacri given Foy-echelon Torm Write the system equations (or Wnich thc niven matrix quamenicc matrix- (Enter each jnswcr tcrns X,Ya Z, and #.) +x+ 2y+ 32 y-2 Zw + 2 (6) Usc back-substitution solvc (nc Syscem (xYr z, W) 4,3 1,3...
5 answers
Da Find Scokan &fa fk4l fow-x-Sxyty 4:(3,4)
Da Find Scokan &fa fk4l fow-x-Sxyty 4:(3,4)...

-- 0.019474--