5

In 2017, the entire fleet of light?duty vehicles sold in theUnited States by each manufacturer must emit an average of no morethan 90 milligrams per mile (mg/mi) of...

Question

In 2017, the entire fleet of light?duty vehicles sold in theUnited States by each manufacturer must emit an average of no morethan 90 milligrams per mile (mg/mi) of nitrogen oxides(NOX) and nonmethane organic gas (NMOG) over the useful life(150,000 miles of driving) of the vehicle.NOX + NMOG emissions over the useful life for one carmodel vary Normally with mean 84 mg/mi and standarddeviation 6 mg/mi.(a) What is the probability that a single car of this modelemits more than 90 mg/mi of NOX + NMO

In 2017, the entire fleet of light?duty vehicles sold in the United States by each manufacturer must emit an average of no more than 90 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 84 mg/mi and standard deviation 6 mg/mi. (a) What is the probability that a single car of this model emits more than 90 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.) probability: (b) A company has 16 cars of this model in its fleet. What is the probability that the average NOX + NMOG level ????¯ of these cars is above 90 mg/mi? (Enter your answer rounded to four decimal places.) probability:



Answers

The mean number of miles driven per vehicle annually in the United States is 12,494 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1290 miles. What is the probability that the vehicle was driven more than 15,000 miles? Less than 8000 miles? Would you buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year?

Going? Ah, start to school. Problem number 61. Ah, we know from the given that, um that meaning mean. Oh, Max. Ah, Liquid won't win before. And standard deviation X, It was no point Open three. This is from the givens. Okay. We also know that on the property for, ah, property for the mean and some of the feeling that mean off and a x A plus b ah, why and equals a and looking blowing boy mean off of experts Be withdrawing by green Old Reich and also on rebellions. Rebellions on OPEC's Except be wind equal e square. Ah, look! The growing boy Variance. Ah x radiance of X Cross me. It's weird. Ah, not growing, boy radiance. Oh, what? These are a properties were I mean and and very insult. Okay, so now we are trying to find the mean off ah of X. We're tryingto find mean off x one, minus Exton and minus x tuned. And this is equal to Yeah. Oh, x one A minus me. And, well, ex cool, Which is equally true? One point for us. One point for 8 to 0. Ah, And for the Sunday the radiation from the baby. Oh, x one minus x two. And this is equally as we know that snuck me in is a square root that's brutal off the Iranians. 20 minutes extreme on and from using this property we can say that Ah, the variance is equal to ah ah equipped to variants of X both variance. All right, record low coefficient a and be in this case is equipped one ah two. And this can be equally square Root off Uh oh Quin Cree school which is the standard deviation stated in the in the evening Plus opened a three s quit and so the front answer would be negative. Naturally will be no point for 143 So this is a mean off X 1162 And this is the Sun division off X one minus x two. Okay, so now we are trying to find a problem. Anything trying for Fine. Um, this is a family. Okay, so now we're front performances it brandy, which is which means of ending. Uh then you minus mean and you wanted me over standard babies. Okay. And we also complete this. Ah, it's venues. Ah, So, uh, we work returning that we find the value off. It's smaller than 1.1. So one point corn hands of some of the Venusian use. Uh huh. Does it is. The square is a very decreased body. They need the world wasn't deviation. So it's 1.1 minus 1.8. This is the value we are trying to find. When a zero, which is in me over the Central Division, she is opened 4 to 443 Yeah. What is it ready for multiples? Didn't really is equal to negative at one point, it might. Now we are trying to find the probability. Um, we're trying to find the probability. Ah, that and then Ah, smaller, thin negative. At one point, it it my ah, or the probability that's is it. And it's bigger than one point 1.8 eight. No. Okay, we're trying to find these probabilities and actually her for that. The smaller than, ah, negative 1.9. If this is a distribution, um, did smaller than 1.9, So we're tryingto find and it's probability. And is it the bigger than 1.89? So we are trying to find this area under the care and these two areas are the same. So we can say that probably it was that this more than negative 1.8 or parole it was that bigger than 1.89 And they are and the same. So it's equal to two month blind by, um Ah, probability. Huh? Hasn't, um, smaller than negative 1.8 on 28 9 Okay. Promoting the the tables to find the value for this probability s o from the table. Ah, we found that the probability for the area under the curve for 20 this'll area in equal tune. Good point. Uh oh. Two, nine four. It was a final answer for that is equal to So it's when the answer was that they worked. Ah, all points. Whole point. Mmm. Why? Eight. Eight. Thank you.

For this problem were given the following table shown to the right part. A asks us to create a joint probability table. To do this, we take the number of favorable outcomes divided by the total number of responses. So for the joint probability of being a US made car, we take 87.4, divided by 657. To get a joint probability of 0.1330 rely truck in US made we take 193.1, divided by 657 to get a joint probability of 6570.2939 We repeat this process for the joint probability of non US made car in for non US made light truck. To get the marginal probabilities, we add up the joint probabilities in each row and column. So for the marginal probability of being a US made vehicle, we do 0.133 plus 0.2939 to get a marginal probability of 0.4 to 69 We repeat this process for non us with a column car and for the column light truck to get all of the marginal probabilities her PS. What do the marginal probabilities tell you about the probabilities associated with the manufacturer in type of vehicle sold? Looking at the marginal probabilities, we can see that non us the cars have a higher probability of being non us than us. Therefore, the probability of a non U. S vehicle is higher. Looking at the columns of car and light truck light truck has a higher probability than car. So therefore, the probability of a light truck is hard hurt. See asks if the vehicle was manufactured by one of the U. S. Automakers. What is the probability that the vehicle was a car and then what is the probability that it was a light truck? So the probability of a car given that it is US made equals the joint probability divided by the marginal probability of being a U. S. Car. The joint probability between being a car and us made is 0.1330 divide about the marginal probability of being US made, which is 0.4 to 69 to give a probability of 0.311 fat. The probability of a light truck given us made equals the joint probability divided by the marginal probability of being US made. This equals 0.2939 Nevada by 0.4 to 69 Do you have a probability of 0.688? Five parte de asks if the vehicle was non us made. What is the probability that vehicle was a car? Was the probability that it was a lie trapped the probability that it was a car? Given this non US mate is equal to the joint probability divided by the probability of it being non us mate, this is equal 2.3478 divided by 0.5731 Do you have a probability of 0.6069? The probability of a light truck given on US made equals the joint probability divided by the marginal probability of being on us, mate, this is 0.2253 vote about 0.5731 to give a probability of 0.3931 party asks if the vehicle was a light truck. What is the probability that it was manufactured by one of the U. S. Automakers? This is the probability of being us made, given that it is a light truck. This is equal to the joint probability divided by the marginal probability of being a light truck. So this equals 0.2939 divided by 0.5192 to give a probability of 0.5661 part F s. What does the probability information tell you about sales? Looking at all of the information, you can say that most of the sales are non US cars, while least of the sales are US cars. This is shown with the marginal probabilities and the probabilities calculated about.

And this question we're told the useful life of a real type of tire is normally distributed with means 50,500 mi and standard deviation in 915 mi. And whereas for the probability that her tire will have a useful life between 57,000 and 58,000 miles, so we're going to convert that to our standard normal random variable so that Z Between nine is .53 10.53, which is the same as probability the less than 0.53 minus, probably TZ less than minus 0.53 And from our table, those values are 27 019 -1981, which is .403. Now in B, we're told that Hamlet pies for such tires, assuming their lifetimes our independence. So this is looking like a binomial distribution. So advise four tires, perhaps for the probability that all four will last for this long. So the probability we have P in our binomial distribution, .403, 8. And so our probability here that all four will last is basically .403, 8 to the power of four, Which gives us .0266.

As you can see, I've got to normal distributions drawn out here. 1st 1 up top is generic. Meaning it's just any time you were told that you have a data set that is normally distributed. This is the type of scenario that you're looking at. Okay, We know from the empirical rule that 60% of our data is kept within one standard deviation. 95% of our data is kept within two standard deviations, and 99% of our data is kept within three standard deviations. I've gone ahead and split those out because we know normally distributed means that are mean or average is smack dab in the middle. So it's splitting everything in half. You can see that 34 on 34 68. So on so forth. I am assuming that you guys understand a basic normal distribution before we're going through with this problem. If all those percentages means nothing to you and you have not been taught H and Eric normal distribution, then you're not going to be able to understand how to apply it to a specific situation like this problem. So before you continue with this video, make sure you understand how I've got those generic percentages before we start trying to apply it here? Okay, Now, assuming that you do understand those looking at this second normal distribution, this represents the actual problem we're doing. We've been told we're talking about the life of car batteries. We were told that the mean is 100,000 miles and that the standard deviation is 10,000. So I've gone ahead and marked out our three standard deviations. I added 10,003 times to the right, subtracted 10,003 times to the left to get my 1st 2nd and third standard deviation away from Army and of 100,000. Okay, Now the question here is asking us what is the probability that you will have a car that you can get a car battery that lasts between 80,000 and 100 and 10,000? Well, okay, let's mark what they're talking about. Then here's 80,000. Here's 100 and 10,000. So it's asking us about this portion this interval of our chart of our data of our graph. Okay, if you understand the generic normal distribution and it's percentages, this problem really isn't that tough. All you have to do is add up each of those slivers each of those portions of the graph. So on the generic one, here's the second standard deviation cause noticed. The 80,000 is on the red. It's the second standard deviation. Here's my positive first standard deviation because the 110,000 is the blue. It's the first standard deviation. So we're talking about this portion, meaning we simply just need to add all three of these percentages together. So that means we're taking 13.5% from the red, plus 34% plus another 34% right. That's the portion of the graph that we're looking at here. If you take 13.5 plus 34 plus 34 that will give you 81.5% or remembering that percent means to divide by 100 81.5 divided by 100 meaning in decimal form, that would give us 0.815 That is actually all we have to do for this one, because it did just ask us for a probability we don't care about the fact that the company makes 20,000 batteries a month because it didn't ask how many batteries this time, it just asked, was the probability. So we're done.


Similar Solved Questions

5 answers
17_ An amount of solid barium chloride, 20.8 g, is dissolved in 100 g water in a coffee-cup calorimeter by the reaction: BaClz (s) Ba?t(aq) + 2C1-(aq) The water is originallyat 25.0 *€ and after the reaction the temperature of the solution is 26.6 "C. (Cs=4.04 J(g?C) for the solution)What is the enthalpy change (AH) associated with the reaction as written?A. + 650 ]B. -650 ]C.-780D. 6500E. -7800 ]
17_ An amount of solid barium chloride, 20.8 g, is dissolved in 100 g water in a coffee-cup calorimeter by the reaction: BaClz (s) Ba?t(aq) + 2C1-(aq) The water is originallyat 25.0 *€ and after the reaction the temperature of the solution is 26.6 "C. (Cs=4.04 J(g?C) for the solution) Wha...
5 answers
Suppose that the credit remaining on phone card (in dollars) is a linear function of the total calling time (In minutes). When graphed, the function gives a line with slope of 0.14_ See the figure below:There is S23.08 in credit remaining on the card after 22 minutes of calls_ How much credit was there after minutes of calls?Remaining credit 308 (in dollars /Calling tIme
Suppose that the credit remaining on phone card (in dollars) is a linear function of the total calling time (In minutes). When graphed, the function gives a line with slope of 0.14_ See the figure below: There is S23.08 in credit remaining on the card after 22 minutes of calls_ How much credit was ...
5 answers
Sample of gas contains 1900 mol of CH(g) and 0.1900 mol of HzO(g) and occupies volume of H5.5L. The following reaction takes place:CH(g) - H,O(g)H-(g) cO(g)Calculate the volume of the sample after the reaction takes place; assuming that the temperature and the pressure remain constant
sample of gas contains 1900 mol of CH(g) and 0.1900 mol of HzO(g) and occupies volume of H5.5L. The following reaction takes place: CH(g) - H,O(g) H-(g) cO(g) Calculate the volume of the sample after the reaction takes place; assuming that the temperature and the pressure remain constant...
5 answers
The function h is defined below:X h() = 1-25Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas8 0D,
The function h is defined below: X h() = 1-25 Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas 8 0D,...
5 answers
Metra train is moving toward the station at speed of 25 m/s: (For perspective. 27m/s about 60 mph) Its horn emits sound of frequency 720 Hz.Calculate the frequency detected by person standing still at the station (Use 345 m/s for the speed of sound;) 772(b) As the train moves away; still blowing its horn at the same frequency as before_ the observer hears frequency of 684 Hz . Calculate the new speed of the train 50.25 mis
Metra train is moving toward the station at speed of 25 m/s: (For perspective. 27m/s about 60 mph) Its horn emits sound of frequency 720 Hz. Calculate the frequency detected by person standing still at the station (Use 345 m/s for the speed of sound;) 772 (b) As the train moves away; still blowing i...
5 answers
9. Volume of a Torus A torus is formed by revolving the region bounded by the circle x2 + y2 1 about the line x 2 (see figure). Find the volume of this "doughnut-shaped" solid (Hint: The integral fl ] x dx represents the area of semicircle.)3 ~.."i| 'i'3|,B < Ji,d /4
9. Volume of a Torus A torus is formed by revolving the region bounded by the circle x2 + y2 1 about the line x 2 (see figure). Find the volume of this "doughnut-shaped" solid (Hint: The integral fl ] x dx represents the area of semicircle.) 3 ~ . . "i| 'i '3| , B < Ji,d...
5 answers
Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers_ xli/3 F1734x3z2/5 X17z320
Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers_ xli/3 F173 4x3z2/5 X17z 320...
5 answers
13. At a given temperature (25 "C) K = 5.8x 10 * for the reaction } , 2NH;(g) COz(g) NCHO(s) HzO(g) Calculate value of K and Kpfor the following reaction at 25"C I/2N,CHO(s) 1/2H,O(g) K: 0.0076; Kp3ILxIO NHs(g) + 1/2COz(g)
13. At a given temperature (25 "C) K = 5.8x 10 * for the reaction } , 2NH;(g) COz(g) NCHO(s) HzO(g) Calculate value of K and Kpfor the following reaction at 25"C I/2N,CHO(s) 1/2H,O(g) K: 0.0076; Kp3ILxIO NHs(g) + 1/2COz(g)...
4 answers
Q3) A circular plate is rotationg with constant angular velocity @ about its axis. On the plate particle moves away from the center with constant speed What is the equation of the path drawn by the particle with respect to the absolute frame Xyz passing through the center of the plate: The initial velocity of the particle is parallel to the X-axis:Plv
Q3) A circular plate is rotationg with constant angular velocity @ about its axis. On the plate particle moves away from the center with constant speed What is the equation of the path drawn by the particle with respect to the absolute frame Xyz passing through the center of the plate: The initial v...
5 answers
The amount of gas adsorbed physically on charcoal(a) increases with pressure and decreases with temperature(b) increases with temperature and decreases with pressure(c) increases with temperature and pressure(d) increases either temperature or pressure.
The amount of gas adsorbed physically on charcoal (a) increases with pressure and decreases with temperature (b) increases with temperature and decreases with pressure (c) increases with temperature and pressure (d) increases either temperature or pressure....
4 answers
Question 4 (7 marks) Melbourne Uni Lodge has decided to provide cup of cold or hot drinks for their tenants to attract them after the Covid pandemic They have determined that mean number of cups of drinks per day is 2.00 with the standard deviation of 0.6. There will be 125 new tenants in the upcoming months_ What is the probability that the new tenants will consume more than 240 cups of drinks per dav?ANSWER:
Question 4 (7 marks) Melbourne Uni Lodge has decided to provide cup of cold or hot drinks for their tenants to attract them after the Covid pandemic They have determined that mean number of cups of drinks per day is 2.00 with the standard deviation of 0.6. There will be 125 new tenants in the upcomi...
5 answers
What do you do first if you are asked to solve a triangle and are given three sides?
What do you do first if you are asked to solve a triangle and are given three sides?...
1 answers
Finding Inverse Functions $A$ one-to-one function is given. (a) Find the inverse of the function. (b) Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line $y=x$ $$ g(x)=x^{2}+1, \quad x \geq 0 $$
Finding Inverse Functions $A$ one-to-one function is given. (a) Find the inverse of the function. (b) Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line $y=x$ $$ g(x)=x^{2}+1, \quad x \geq 0 $$...
5 answers
Let XN(0,4) where 0 has prior density N(2,8)Find the prior probability that 0 > 6. Find the posterior density of 0. If X 2 find the posterior probability that 0 > 6_ Find the Bayes' estimator of 0. Is the prior distribution conjugate prior? Explain.
Let X N(0,4) where 0 has prior density N(2,8) Find the prior probability that 0 > 6. Find the posterior density of 0. If X 2 find the posterior probability that 0 > 6_ Find the Bayes' estimator of 0. Is the prior distribution conjugate prior? Explain....
5 answers
Determine whether the equation is exact: If it is, solve tne DE:(2ysinxcosx - Y+2y?e"hdx (x-sin?x - 4xyerh)dy O 2ex? +ysin?x+xy=C2ety? +ysin?x - xy= C 0 2e*?y+ysin?x-xy-€ 0 2exy _ ysin?x-xy= €
Determine whether the equation is exact: If it is, solve tne DE: (2ysinxcosx - Y+2y?e"hdx (x-sin?x - 4xyerh)dy O 2ex? +ysin?x+xy=C 2ety? +ysin?x - xy= C 0 2e*?y+ysin?x-xy-€ 0 2exy _ ysin?x-xy= €...
5 answers
Uce the calaulato Droyidedsolve the followlng problemsConsiderLdlstdbution wlth _ deorccsolueedam comdutl1.18). Round your ansryerleastthtecdecma placesConslder Oacnscanoukon24 degrees cftreedom Find tne valuc of € such that P (-e<t<e) 0,95_ Rauna Your JnsweiIcast threardeelmalL.18)
Uce the calaulato Droyided solve the followlng problems Consider Ldlstdbution wlth _ deorccsolueedam comdutl 1.18). Round your ansryer leastthtecdecma places Conslder Oacns canoukon 24 degrees cftreedom Find tne valuc of € such that P (-e<t<e) 0,95_ Rauna Your Jnswei Icast threardeelmal ...
5 answers
PDF Preserved Horseshoe Crab PhotosStation G2Chie Le 01 rentraiske €t neriesncsOrd
PDF Preserved Horseshoe Crab Photos Station G 2 Chie Le 01 rentraiske €t neriesncsOrd...
5 answers
Find the polar coordinates; 0 < 0 < 21 and rs0, of the following points given in Cartesian coordinates(6,613 ) 613,6)(-213,2) d. (15,_ 8)
Find the polar coordinates; 0 < 0 < 21 and rs0, of the following points given in Cartesian coordinates (6,613 ) 613,6) (-213,2) d. (15,_ 8)...

-- 0.070576--