5

Let X be the time taken to assemble a car in a certain plant:Xis a random variable having a normal distribution of 30 hours and a standard deviation of 4 hours.Ques...

Question

Let X be the time taken to assemble a car in a certain plant:Xis a random variable having a normal distribution of 30 hours and a standard deviation of 4 hours.Question:What is the probability that a car can be assembled in period of time greater than 41 hours?Write the full answer with 4 digits after the decimal point: For example, 0.7821 or 0.3523.

Let X be the time taken to assemble a car in a certain plant: Xis a random variable having a normal distribution of 30 hours and a standard deviation of 4 hours. Question: What is the probability that a car can be assembled in period of time greater than 41 hours? Write the full answer with 4 digits after the decimal point: For example, 0.7821 or 0.3523.



Answers

Manufacturing time The assembly time in minutes for a component at an electronic manufacturing plant is normally distributed with a mean of $\mu=55$ and standard deviation $\sigma=4 .$ What is the probability that a component will be made in less than one hour?

So in this question, drives to find the probably the randomly selected automobile workers were ex lesson four yards per week. So we can read that as the probability X less than where X is the number of hours. Automobile workers in this question were also given a hint, which is that the distribution is approximately normal, which means that we can use this standard distribution formula. Z is equal to thanks over six. And the question Rosa, given that the average number of hours MIA is equal to 40 three, said hours on that the standard deviation Sigma is equal to 1.6 to censor China solve for probably even number of eyes listened. 40. We can put 40 into our equation. So for corresponding Z value So just 40 minus 40 3.7 over six disease, which is the same thing that's right, native to seven over 106 h is equal to think it is 2.31 to 5, so we can run that to two decimal places to get negative 23 and then we're gonna be doing is looking for the corresponding probably for this value in this too. Do that beginning get Teoh you one's for which is their final chance

What's the chance of having to work overtime to complete the service and all the cars? While the central limit theorem will help us determine that When we take our sample of 50 cars, They're going to be normally distributed with their average being pretty close to the population average, which is 1.4 hours and that our standard deviation of all those little samples, what is going to be the Standard deviation for the population, which is .7 divided by the square root of our sample size, which is 50 And .7 divided by the square root of 50 is .099. So I'm gonna number my bell curve up and down by .099, And now we get a picture for what's happening here repeatedly taking samples of 50. Um, we want the probability of having to work More than 1.6 hours per car. So I'm going to find 1.6 here on our number. Languages just passed two standard deviations above the mean, and we want to figure out this probability working more than 1.6 hours, so we'll use our we'll get our Z score for that 1.6 minus the average, Divided by our standard deviation of .099 will equal .2, divided by .099, Which is 2.02. And now we'll look up that number in our standard normal probability table in the back book, Which is .9783. But remember that .9783 is to the left of this marker at two point oh two. So we for our probability we're gonna need to do one minus 10.9783 which will equal, yeah, .0217. So 2% chance of working overtime.

We're keeping a probability function pft. And in this function, T is the number of minutes and P is the probability that the event will occur within that number of minutes within T minutes. And our task is to determine after how many minutes so t equals what for the probability Teoh equal 50% which 50% is 50 out of 100 which is 1000.5 and then we're also tasked with determining after how many minutes the probability will have gotten up to 80% which is 80 out of 100.8. So we're gonna have to do the same thing twice. Why not derive a formula t in terms of P, and then we could use that formula twice. That would be more efficient. So we're going to take our our probability formula and solve it for T. So the first thing we're gonna do is subtract one from both sides, and then we're also going to multiply both sides by negative one, and that will isolate our exponential. And then we're gonna take the natural log of both sides. So while we're at it, let's distribute this minus one negative P +11 minus p is equal to the natural log of E to the negative 0.15 t. So what do you take a longer of them oven exponential. If they both have the same base, the result you get is the exponents. Natural log is law based E. So that's the case we have here. The natural log of E to the negative 0.15 t is negative 0.15 t. So to finish solving for tea, we're gonna divide both sides by negative 0.15 So our formula then is natural log of one minus the probability divided by negative 0.15 That's how many minutes. So now we can go and easily find out the number of minutes so T is gonna equal to the natural log of one minus p, which in this case is 10.5. Divide by negative 0.1 five. And with a little help from our calculator, we've determined that that is 4.6 to minutes. So after 4.62 minutes, the probability that the event will have occurred is 50%. That will do the same thing. But this time we want to know how many minutes? For 80%. So natural log of one minus 10.8, divided by negative 0.15 can. With a little help from our calculator, we determined that it's 10.7 three minutes.

All right. So we're visiting burger king and we're looking at the rate of cars Through the drive through between the hours of noon and one p.m. And A random sample of 41 hour time periods between noon and one were taken. And that had to mean at 22.1 as the number of cars arriving. So why is the assembly distribution normal or approximately normal? Well, Even though we don't know anything about the population, we don't need to because the central limit theorem says as long as the sample size is greater than 30, which this is it's It's equal of 40, then that means the sampling distribution has Yeah. And approximately normal distribution. So there you go. Part B. We're gonna find the mean and standard deviation of the sampling distribution. Uh The mean of the sampling distribution is one to which is the population. So, innovation. And the standard deviation of the sample distribution is called the standard of the mean, which is equal to sigma over route. And so in this case is to whoops Route 20 over route 40, which is equal to root root of a half or one of two. And we want to know the probability that a random sample of 40 When our time periods gives a mean of at least 22.1 car. So it's Greater than 22.1 cars. And is this unusual? What can we conclude? Well, let's before you make conclusions, let's figure out what the probability is. So we need the Z. Score, which is given as X. Bar minus mules over. Well, it's actually meat exports. I've Over this same over route 10 says that uh the immune uh new except expire are the same. So numerically is all good. But notation rises Think the more proper one. So we'll do tool C22.1 -20 all over route one half, which ends up giving us a Z score of 297. And we want to be greater than that. So giving a good picture, it's going to look like this Is the mean of 20 into 22 is about here 22.1s roughly here. And then we want this read portion which I'm shading in here in the Z score would of course this 297 would correspond with 22 1 on the normal curve with immune of zero and the standard a normal curve. And we know the probability of that. So we would we're gonna do a little bit of complementary work. So we want the probability that the Z is greater than 297. But Z tables give us The area up to that point. So we need to do the complement of that. So we need of what we're looking for, one minus the probability that Z is less than 2.97 which is going to be equal to 1 -199. So this area which I'm going to be shading and blue. Yeah, all that stuff, This is .999 and we want this red part which is going to end up being .001. And so this is very unlikely. So is this result unusual? Or what's the probability? The probability is .001. Is this unusual? It's very unusual because the probability is so low. Very unusual. Although in statistics vary can be kind of vague. So, you know, it will just say this is unusual. Mhm unusual. What might we conclude from this? Well, this would tell us that there was a rush. Maybe this was a crazy lunch hour of So the or maybe that we got the desert crazy rush. That maybe there was a event around that burger king. So you had a lot of people there Or you know what? Maybe there was just a A crazy sample of 40 days. Like there's just somewhere like that. So there's a those are some things we conclude that we could conclude. So there you go.


Similar Solved Questions

5 answers
Q5 Use ODE methods to solve U,~U,=5, U,(,V)=3y',U(x;O) =
Q5 Use ODE methods to solve U,~U,=5, U,(,V)=3y',U(x;O) =...
5 answers
Solve each triangle ABC having Round_your answer the given information; if possible using significant digits_A=B =C=82.2" C = 7.62 cma=10.9 cmb =
Solve each triangle ABC having Round_your answer the given information; if possible using significant digits_ A= B = C=82.2" C = 7.62 cm a=10.9 cm b =...
5 answers
Flnd the volume of the solid generated bY revolving the regicn bounded by the graphs the equations about the Iine
Flnd the volume of the solid generated bY revolving the regicn bounded by the graphs the equations about the Iine...
5 answers
SunflowerPanel APanel B610Corn seedlingPanel €Panel D
Sunflower Panel A Panel B 6 10 Corn seedling Panel € Panel D...
5 answers
Which structure I5 consistent with the mass spectrum shown? (5 polnts)CH) BrEntcr Your Answer:Draw second resonance structure Which only has one atom with fonmal charge and the carge Is pot on a @ points)co" CHiChjCreate Oscur Skolch Answer
Which structure I5 consistent with the mass spectrum shown? (5 polnts) CH) Br Entcr Your Answer: Draw second resonance structure Which only has one atom with fonmal charge and the carge Is pot on a @ points) co" CHi Chj Create Oscur Skolch Answer...
5 answers
3_ Let p2(r) be the quadratic polynomial interpolation of f (x) at € 0,h, 2h, and then derive a quadra- 3h ture Ih for I = f(z) dx. Use a Taylor series expansion of f (x) to prove that3 I _ Ih h'f(8) (0) + O(h5)
3_ Let p2(r) be the quadratic polynomial interpolation of f (x) at € 0,h, 2h, and then derive a quadra- 3h ture Ih for I = f(z) dx. Use a Taylor series expansion of f (x) to prove that 3 I _ Ih h'f(8) (0) + O(h5)...
5 answers
The amount in an account grows at a rate of &% compounded continuously:How long will it take for the amount to double?How long will it take for the amount to increase by 50%?
The amount in an account grows at a rate of &% compounded continuously: How long will it take for the amount to double? How long will it take for the amount to increase by 50%?...
5 answers
Conccntralion; million, Ppm: Le8] sample of ground walcr is found t0 contain 0.0107 1 Calculate the concentration 1
conccntralion; million, Ppm: Le8] sample of ground walcr is found t0 contain 0.0107 1 Calculate the concentration 1...
1 answers
If the cable is subjected to a maximum force of $P=50 \mathrm{kN},$ select the lightest $\mathrm{W} 310$ shape that can safely support the load. The beam is made from steel having an allowable normal stress of $\sigma_{\text {allow }}=150 \mathrm{MPa}$ and allowable shear stress of $\tau_{\text {allow }}=85 \mathrm{MPa}.$
If the cable is subjected to a maximum force of $P=50 \mathrm{kN},$ select the lightest $\mathrm{W} 310$ shape that can safely support the load. The beam is made from steel having an allowable normal stress of $\sigma_{\text {allow }}=150 \mathrm{MPa}$ and allowable shear stress of $\tau_{\text {all...
5 answers
Points) Belowfirst order linear differential equation:0 _ 168 = t_6For each initial condition given below; using the Existence and Uniqueness Theorem, the widest where the equation has one solution < t < 6 Find the range in the form:Note: Your answers are t 4or 4 < t < 4ort > should be written in the form:y(-5) = 0.5.y(-2.5) = 6.4.y(o) =0.y(4.5) = 1.7.9(14) = 1.7.Note You can eam partial credit on this problem
points) Below first order linear differential equation: 0 _ 168 = t_6 For each initial condition given below; using the Existence and Uniqueness Theorem, the widest where the equation has one solution < t < 6 Find the range in the form: Note: Your answers are t 4or 4 < t < 4ort > shou...
5 answers
This Coversio Con be Camed oub in 3 Step' Ladicte the two Steps 8 rchanismOHOHOH
This Coversio Con be Camed oub in 3 Step' Ladicte the two Steps 8 rchanism OH OH OH...
5 answers
Solve the given differential equation 4y +5 dy d2 +4y = cet ~8 dcF4r 0v = C1e +C2e 0v = Q1e-&r +C2e ov =91e~Lr +C2e 0" =40 F4r +C2erer 0O10e' ~2 1010O100et 10Te- 10OU
Solve the given differential equation 4y +5 dy d2 +4y = cet ~8 dc F4r 0v = C1e +C2e 0v = Q1e-&r +C2e ov =91e~Lr +C2e 0" =40 F4r +C2e rer 0O 10 e' ~2 10 10O 100 et 10 Te- 10 OU...
5 answers
Adcante Eedneo batirnn cm thcVht Lettui 44etIecua
Adcante Eedneo batirnn cm thc Vht Lettui 44et Iecua...
1 answers
{cnsider ie [nudlicn J(#) Find the sexxnd] degree Taylor polynomial P(#) aboul = _Whal acc thee glternaling "erie: eror hund sey gbout P(0.CS)2Whal doe; the alternaling seriex: error #Oun sgy &tout F(-0.03)7Whal &ror dlces :he Legrange Error Bouud give Iur Ri(r) at = _
{cnsider ie [nudlicn J(#) Find the sexxnd] degree Taylor polynomial P(#) aboul = _ Whal acc thee glternaling "erie: eror hund sey gbout P(0.CS)2 Whal doe; the alternaling seriex: error #Oun sgy &tout F(-0.03)7 Whal &ror dlces :he Legrange Error Bouud give Iur Ri(r) at = _...
5 answers
Fill in the blanks below. A block with mass M = 0.5 Kg attached to a spring. If the spring mass system is described by position x(t) = 0.15 m cos(3t). Find Spring constant K------Period T-------V max----x(t)-----at t =0.35 s
fill in the blanks below. A block with mass M = 0.5 Kg attached to a spring. If the spring mass system is described by position x(t) = 0.15 m cos(3t). Find Spring constant K------ Period T------- V max---- x(t)-----at t =0.35 s...
5 answers
Csc2 0 sin? 0 = 1
Csc2 0 sin? 0 = 1...

-- 0.056379--