5

CAalDONYoci ND Distendumon Normal distribution: Finding scd @nomally dlstributed mean of 64,5 Inches and standard_devlation Suppose that thc heights of adult women ...

Question

CAalDONYoci ND Distendumon Normal distribution: Finding scd @nomally dlstributed mean of 64,5 Inches and standard_devlation Suppose that thc heights of adult women the United States women How tall (In Inches) Jennlfer? camy - ouc inlermt coate ot 2.4 Inches; Jennifer Is taller than 759 of the populatlon of U.S: places Round Your Jnswver declmal place. computatlons at least four decimalIncnet

CAalDONYoci ND Distendumon Normal distribution: Finding scd @ nomally dlstributed mean of 64,5 Inches and standard_devlation Suppose that thc heights of adult women the United States women How tall (In Inches) Jennlfer? camy - ouc inlermt coate ot 2.4 Inches; Jennifer Is taller than 759 of the populatlon of U.S: places Round Your Jnswver declmal place. computatlons at least four decimal Incnet



Answers

Heights of Female Students. Refer to Example 6.1 on page $256 .$ The heights of the 3264 female students attending a midwestern college are approximately normally distributed with mean 64.4 inches and standard deviation 2.4 inches. Thus we can use the normal distribution with $\mu=64.4$ and $\sigma=2.4$ to approximate the percentage of these students having heights within any specified range. In each part, (i) obtain the exact percentage from Table $6.1,$ (ii) use the normal distribution to approximate the percentage, and (iii) compare your answers. a. The percentage of female students with heights between 62 and 63 inches. b. The percentage of female students with heights between 65 and 70 inches.

In problems event. We have the mean of college German, which equals 65 inches. And assuming the height of women are normally distributed like this, we have the standard division of this distribution, which equals 20 2.5 inches. We knew that the normal distribution is about the mean where the mean here is 65 inches we have here in inches here is 65 and the normal distribution is centered at the mean. Based on this information, you want to answer from party to birth, the for body we want to calculate the percentage of women which are taller than 65 inches taller than 65 inches, means we want to calculate the area under the normal distribution. Here, all this area, which equals half then percentage equals 50%. For both to be, we want to calculate a percentage of women who are shorter than 65 inches, which means we want to calculate this area, which is half the total area, and the total area is one. Then the area is half and the percentage will be 50%. This is from the definition of the mean, 50% are greater than the mean or taller than the mean, and the other 50% are shorter than the mean full bar. See, we want to calculate the percentage of women who are between 60.5 inches and 67.5 inches. If you noticed these values, we can rewrite it as between 65 minus 2.5 inches and 65 plus 2.5 inches. And in the normal distribution, we will be here at new minus sigma and here, new plus sick. We want to calculate the area with the blue color. This area equals 68 percent from the definition off the normal distribution. Bye. Deviating from the mean by a value off minus sigma and blah sigma. We have the percentage equals 68 person for Barney they owned to calculate the percentage of women who are between 60 inches and 70 inches. Again, we can rewrite these values Toby from 65 minus five or minus two, multiplied by 2.5 and 65 plus two multiplied by 2.5, which means we want to calculate this area. The area between New Plus two Sigma and new minus two Sigma this area with the red color. We're represents representative of women between 60 inches and 70 inches from the definition of normal distribution. This area equals 95% or his area equals 4.95 and in percentage is it's 95. There's vintage, and these are the final answers off our problem.

Hey, it's Clearasil. New rate him. So we know the density function for a normal distribution of a random variable X with the mean and standard deviation. So we get the mean to be equal to 65.5 and the standard deviation to be equal to 2.5. So given this data, we're just gonna plug it into our equation. One over 2.5 square root of two pi e so negative X minus 65.5 square, divided by 12.5. So we're gonna look for when it's taller than 65 68 inches. So excess bigger or equal to 68. So we get the integral from 68 to infinity, and we just plug in this equation, which is one over 2.5 square it of to pine. Okay, so negative X minus 65.5 square divided by 12.5 x. And we get around 0.16 which is equal to 16%. For part being, we're gonna d'oh! So five feet one There's 61 inches and five feet and four inches. It's 64 inches. So it's the probability that access between 61 in 64 so this is into grow from 61 64 for one over 2.5 square root of two pi e. It's the negative x minus 65.5 square over 12.5 t x when we get around 0.23 832

Hey, it's clear someone knew Marie here. So what I didn't really know is that we're given the mean, which is 65.5 in the standard deviation, which is 2.5. And I just plugged it into the density function for normal distribution off a random variable X with the mean and standard deviation so far apart, they were looking for a taller than 68 inches. So this is gonna be then to grow from 68 to infinity. We just plug in our equation, which is one over 2.5 square root of two pi. He'd the negative x minus 65.5 square over 12.5 d x, which gives us around 0.16 so it's 16% for Part B. We're looking at five foot one and five foot four. It gives us 61 inches and 64 inches, respectively. So it's from 61 2 64 So we have the same thing, but our intervals changes from 61 to 64. One over 2.5 square root of two pi peaks. The negative x minus 65.5 square over 12.5 t x, which is equal to 0.23832

In question 36. It says the height of young men following normal distribution with mean of 69.3 inches. So would you say that mean of men 69.3 and a standard deviation to be 2.8? We also know that the height of young women following normal distribution with mean of 64.5 and a standard deviation of 2.5 part A says let em be the height of a randomly, said a young man. W be the height of randomly said a young woman described the shape center and spread of L minus w so, uh, shape center spread. We basically want to find the, um, the shape of the distribution, which it tells us that the males come from a normal distribution and the females also come from a normal distribution. So we know that the shape of M minus W is approximately normal. The center would be the mean. We want to know what does the mean of l minus. W Well, that is simply mean of M minus mean of W, which would be 69.3 minus 64.5. You get the mean of M minus w to be 4.8, and that would be the center spread is referring to the standard deviation standard deviation of l minus stop. You would be well, we can't just simply subtract their Senate deviations. But if we took the Senate Center deviation of male minuses, center, deviation of female or W in this case, we confined, um, the standard deviation of these two combined distributions by finding the variants combining the variant says, and then take that down to a standard deviation. So the trick here is to find the variance by squaring, squaring when you square anything that changes that to a positive. And then, in order to turn that back into a Senate deviation, we will take the square to this final answer. So we have 2.8 squared plus 2.5 squared. That gives us 14.9 That is our center deviation. In order to take that to our story, that is our variance. In order to take that to our center deviation when you take the square root of 14.0 nan, that is 3.75 for Part B. It says find the probability that a randomly selected young man is at least two inches taller than a randomly selected young woman. So find the probability that a randomly selected we'll just say M minus w is at least two inches taller than a young woman. Now you could put greater than to or greater than equal to two. It doesn't matter here. We know that this is a normal distribution so we can use our normal CDF command in our T 80 three or 84 calculator. We need our lower bound. Our upper bound are mean in our standard deviation. We know that our mean from earlier is 4.8, and our standard deviation is 3.75 If you want to figure out the lower and upper bound, the easy way to do this is to kind of draw the picture of what's going on. 4.8 center. We need to know what's the probability of greater than to swing it to somewhere over here to the left of 4.8, and greater than everything over here to the right, so your lower and upper bounds, where you start shading in where you start coloring so lower bound is to upper bound. Technically, never ends. Well, just play in this, uh, to represent infinity. So take that to your calculator command. Type that in and we get approximately 0.77 24


Similar Solved Questions

5 answers
The portion of the graph o y = %22 _ ~4 shown below_
The portion of the graph o y = %22 _ ~4 shown below_...
5 answers
When a piece of copper, at a temperature of 256 %C,is added to 255 grams of water,ata temperature of 20.0 C,the final temperature of the resulting mixture is 24.0 oC- If the Speefic hatof copper is 0.385 Jg K; what was the mass of the copper? 0.0405 g (6) 47.7 8 99.2 g 219 g
When a piece of copper, at a temperature of 256 %C,is added to 255 grams of water,ata temperature of 20.0 C,the final temperature of the resulting mixture is 24.0 oC- If the Speefic hatof copper is 0.385 Jg K; what was the mass of the copper? 0.0405 g (6) 47.7 8 99.2 g 219 g...
5 answers
At t the switch $ is closed with the capacitor Urk harged. If € 30 HF, capacitor alt 0.3 sec ?50 V, and R 10 k what| the potential dltferen;Select one: 45.8 vb. 31.6 =20,610.3
At t the switch $ is closed with the capacitor Urk harged. If € 30 HF, capacitor alt 0.3 sec ? 50 V, and R 10 k what| the potential dltferen; Select one: 45.8 v b. 31.6 = 20,6 10.3...
5 answers
9. TEM modes can propagated in & rectangular waveguide in Z-direction, when HFEzF0.TrueFalse
9. TEM modes can propagated in & rectangular waveguide in Z-direction, when HFEzF0. True False...
5 answers
Y=-1Y= 1X=-1 X=10.25 200.35
Y=-1 Y= 1 X=-1 X=1 0.25 20 0.35...
5 answers
Erenat uln Emam !HelttooaV,0oov CodioiPurt AEnettT 7Lnettro Ketatiteewiriq orderWvos Alt7207,355.131KelerAnuartnIncoleci;Aunn; ? atte Inote (citWicmrig{Renmna AaaiHoacael
Erenat uln Emam !Heltt ooaV,0oov Codioi Purt A EnettT 7 Lnettro Ketati teewiriq order Wvos Alt 7207,355.131 Keler Anuartn Incoleci; Aunn; ? atte Inote (citWicmrig {Renmna Aaai Hoacael...
5 answers
Thamu Di 4.5 53e5 comed wBTer fot TDe pariod 2007-2014 couli #= appraxir ated by 4} = 0oar, 0.z0k 448 bllben gallnat pet Vtt (ftsn whor? $ Is tima (72313 since Uw atant 0l 200/ + Extlmnute Wie ~veirq0 unnual jalet bottleu Mates Ovnt tho purnu 7o0l - u Mdn Yaikria pEt Yeuimnimton unllunatnal Ynd(6) Comipute Ltn 5r4 movlrig 4vezq8 0 # (You need not(cLiiout ulmpldylng the Jhawor Mrt (0}4 sav what klnd Funcuan the rhovllg avel44" comuntIlnczrMzdteilc
Thamu Di 4.5 53e5 comed wBTer fot TDe pariod 2007-2014 couli #= appraxir ated by 4} = 0oar, 0.z0k 448 bllben gallnat pet Vtt (ftsn whor? $ Is tima (72313 since Uw atant 0l 200/ + Extlmnute Wie ~veirq0 unnual jalet bottleu Mates Ovnt tho purnu 7o0l - u Mdn Yaikria pEt Yeui mnimton unllunatnal Ynd (...
5 answers
The H-X bond strength decreases in the series HF, HCl, HBr, HI. Explain this in terms of the molecular structure of the molecules.
The H-X bond strength decreases in the series HF, HCl, HBr, HI. Explain this in terms of the molecular structure of the molecules....
5 answers
Question 24ptsFor the given stem and leaf plot find the medain and Made;Meac Jan-32. Mode-35Modaln-35, Modar 32Medaln" 29, Mode- 24Meclan-14.5. Moder 51
Question 24 pts For the given stem and leaf plot find the medain and Made; Meac Jan-32. Mode-35 Modaln-35, Modar 32 Medaln" 29, Mode- 24 Meclan-14.5. Moder 51...
1 answers
Use a graphing calculator to find the rectangular coordinates of $\left(2,-\frac{\pi}{5}\right) .$ Round to the nearest thousandth.
Use a graphing calculator to find the rectangular coordinates of $\left(2,-\frac{\pi}{5}\right) .$ Round to the nearest thousandth....
5 answers
Suppose the number of typos on a page of document follows the Poisson distribution with parameter1 = 05Answer the following questions.(a) What is the probability of having no typos on a page?(b) What is the probability of having at least 3 typos on a page?(c) What is the probability of having no typos on a 5-page document?
Suppose the number of typos on a page of document follows the Poisson distribution with parameter 1 = 05 Answer the following questions. (a) What is the probability of having no typos on a page? (b) What is the probability of having at least 3 typos on a page? (c) What is the probability of having n...
5 answers
A filament has resistance of 0.10 W at 20"C. If the resistance becomes 0.14 W when the temperature of the filament increases to 90*C, the temperature coefficient of resistance for this material is 5.7 S1*C. 5.7 10-4/'C, 4.4 10-3/8C. 4.4 10-4/C.
A filament has resistance of 0.10 W at 20"C. If the resistance becomes 0.14 W when the temperature of the filament increases to 90*C, the temperature coefficient of resistance for this material is 5.7 S1*C. 5.7 10-4/'C, 4.4 10-3/8C. 4.4 10-4/C....
5 answers
How do the uncouplers of oxidative phosphorylation work? Describe the molecular mechanism
How do the uncouplers of oxidative phosphorylation work? Describe the molecular mechanism...
5 answers
Write the expression as the sine_ cosine tangent of an angle_ sin 330 cos 1608 cos 330 sin 1609
Write the expression as the sine_ cosine tangent of an angle_ sin 330 cos 1608 cos 330 sin 1609...
5 answers
Determine the structure of the following compound, based on molecular formula and IR and 'HNMR spectra. Show all your reasoning:Co
Determine the structure of the following compound, based on molecular formula and IR and 'HNMR spectra. Show all your reasoning: Co...
5 answers
An unknown radioactive element decays into non-radioactive substances. The rate at which the element decays is proportional to the remaining amount of the element:In 320 days the radioactivity of a sample decreases by 76 percent:What is the half-life of the element?Half-life is 155.0327(days)How long will it take for sample of 100 mg to decay to 43 mg?Time needed is 187.5489(days)
An unknown radioactive element decays into non-radioactive substances. The rate at which the element decays is proportional to the remaining amount of the element: In 320 days the radioactivity of a sample decreases by 76 percent: What is the half-life of the element? Half-life is 155.0327 (days) Ho...
5 answers
Unproctorcd Placement AssessmentDuc FridayThe one-to-one functions g and h are defined a5 follows ((-8, 7). (-5, 9). (~2. 8). (8.h(x) = 3x &Find the folloviing"n)(e)Dontt KnowSubmit
Unproctorcd Placement Assessment Duc Friday The one-to-one functions g and h are defined a5 follows ((-8, 7). (-5, 9). (~2. 8). (8. h(x) = 3x & Find the folloviing "n)(e) Dontt Know Submit...
5 answers
The point P(6, 2} lies on the curve5 _ XIf Q is the pointfind the slope of the secant line PQ (correct to six decimal places) for the following values of x5 _5.95.99(iii) 5.999 mpQ(iv) 5.9999 mpQ6.1(vi) 6.01(vIi} .001(vil ) 0001(b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(6, -2)_Using the slope from part (b); find an equation of the tangent line to the curve at P(6, -2) _mpompompQmpqmpompo
The point P(6, 2} lies on the curve 5 _ X If Q is the point find the slope of the secant line PQ (correct to six decimal places) for the following values of x 5 _ 5.9 5.99 (iii) 5.999 mpQ (iv) 5.9999 mpQ 6.1 (vi) 6.01 (vIi} .001 (vil ) 0001 (b) Using the results of part (a), guess the value of the s...
5 answers
~40` -1 -1 31 what is the value of y -1 = 35Consider the system Az = b with % =and bIf A-1A 25 B. 31 C. 2 D. 37 E. 18Reset Selection
~40` -1 -1 31 what is the value of y -1 = 35 Consider the system Az = b with % = and b If A-1 A 25 B. 31 C. 2 D. 37 E. 18 Reset Selection...

-- 0.023293--