5

Education The scores on a national exam are normally distributed with a mean of 150 and a standard deviation of $16 .$ You scored 174 on the exam.(a) How far, in st...

Question

Education The scores on a national exam are normally distributed with a mean of 150 and a standard deviation of $16 .$ You scored 174 on the exam.(a) How far, in standard deviations, did your score exceed the national mean?(b) What percent of those who took the exam had scores lower than yours?

Education The scores on a national exam are normally distributed with a mean of 150 and a standard deviation of $16 .$ You scored 174 on the exam. (a) How far, in standard deviations, did your score exceed the national mean? (b) What percent of those who took the exam had scores lower than yours?



Answers

Education The scores on a national exam are normally distributed with a mean of 150 and a standard deviation of $16 .$ You scored 174 on the exam. (a) How far, in standard deviations, did your score exceed the national mean? (b) What percent of those who took the exam had scores lower than yours?

The national average for the math portion of the College Board's S A. T is 5 15 The College Board periodically re scales the test scores, such that the standard deviation is approximately 100. Answer the following questions using the a bell shaped distribution and the empirical rule for the verbal test scores. So we've got a a national average, so our average is shown with X, but the line over it and that's it. Five 15 with a standard deviation of 100. So if we use your typical bell curve here, where right here, this would be your average at 5 15 and then one standard deviation above the standard deviation is 100. So you just add the standard deviation of what you had their need out of six 15 another standard deviation 7 15 and then our final standard deviation. You usually do three standard deviations above and then three below 3 15 and then one more to 15. I'm still getting used to this program, so that's why the handwriting's not fantastic. So port A. That's an A not a nine. Ah, what percentage of students have an S a T math score Greater than 6 15 Well, first thing we want to understand is that this chunk right here represents 34% 0 hang on. Sorry. Let's just change that to smaller area. This is about 34%. This is also a 34% chunk making this entire section right here. 68% of you know of people. But what this represents is 68% of people that take the S A T usually score with within 415 as their score and 615 is their score 34% from here to here. On the other, 34% are from here to here. Um, over here, this little chunk right here is going to be at 13% as is, actually, let's use a different color for that in my classroom. I like to color code, so let's go ahead and color code. This is a 13%. This one is also 13%. So if you were to take all of this and you have 68 through this part plus 13 which is, um, 81 plus another 13 which is 94. So 94% of people well usually score between 3 15 and 7 15 on their exam and then to person. So sorry again. Another color. We want 2%. 2% here, 2% here. Meaning? I'm gonna go underneath for this just so that I have enough space. Meaning that so 94 plus 2 96 plus no. To 98% of people. 98% of people score between 215 and 2815. So that is all important to know, to be able to answer these four parts right here. So what percentage of students have an ace and s a C mask or greater than 6 15? So six fifteens right here. And we want everything greater than that. Right? So we've got the 68%. What? Well, here, let's go this way. We've got 100% of people fall under this curve, and then that means that 100% minus the 13 minus the two is some 100 miles. 15 is about 80% 35%. And then there's, like, 0.1% over here. So I'd say that's negligible. Your most people aren't going to be out here way up here or way down here. So we'll say approximately 85% are Ah. Okay, 85% score lower than that. So 15% approximately 15 percent. The students score 6 15 or greater on the S. A T. Part B is asking what percentage of students have an S A T math score greater than 7 15 So now we're looking here. That's about 2%. So about 2% a student score greater than 7 15 So you can see the questions they're going actually relatively quickly, because we were able to set this whole chart up, and that's pretty much where all our works gonna be. What percentage of students have an S A T mask or between 4 15 and 5 15 So I'm just going to race some of this. So if you needed to watch or see any of that, you can just go back in the video eso between 4 15 and 5 15 What percentage of students have an S a T mass score between here and here? Well, between 4 15 and 5 15 is 34%. So about 34% of students score between 4 15 and 5 15 on the math portion of the S a T. Then finally, part D Ah, What percentage of students have an S A T math score between 3 15 and 6 15 So again, let's just go ahead and get rid of this line here so that we don't have too much going on here. So between 3 15 and 6 15 So you take all those percentages in there. He got 13% up there. I'm sorry. That's gonna 13%. You got a 34% and another 34%. That 68% plus 13. That would be 81%. So about 81% of students score between 3 15 and 6 15 on the S A T math test.

The national average for the math portion of the College Board's S A. T is 5 15 So we want to indicate that we have our national average or mean of 5 15 That's our average score. The college board periodically re scales the test scores such that the standard deviation is approximately 100. So standard deviation is about 100. Answer the following questions using a bell shaped distribution and the empirical rule for the verbal test scores. So we want to get our standard deviation or are bell shaped curve drawn in here. Get a nice curve going here. Oh, right. And then you want to draw a line straight down the middle? That represents that was a really bad line. Let's get Go ahead. Redo that. Here we go. That right there represents your mean or your average. Now it tells us that are meaner. Our averages 5 15 So we already have this number here and then you're going to draw three standard deviation lines. But ah, further like above that on three standard deviation lines below it. So this line here is our average minus one standard deviation are averages 5 15 standard deviation is 100. So 5 15 minus 100 is 4 15 This is your average minus two standard deviations. So 5 15 minus 100 twice or minus 200 p 3 15 and then our average minus three Standard deviations which will be to 15. And over here you'll have your average plus a standard deviation. Your average plus two standard deviations and your average plus three standard deviations. Just be 6 15 7 15 and 8 15 Now, in this portion, here we have 34%. What does that 34% mean? That means that 34% of the people that take the the S A T math test score between 415 and 515. Additionally, this chunk is also 34% making right here. The middle chunk of this bell curve is 68%. So 68% of people that take this test score between 4 15 and 6 15 The next boxes outside that this be 13% and 13%. And just like thes, that means 13% of people scored between this score, this score or this score in this score and overall from here A whips. Let's try that again. From here, all the way over to here, You've got 94% of students score between 3 15 and 7 15 And finally, you've got this box here at 2% in this box here at 2% ultimately making from here over to here, 98% of people, 98 percent of people. So 98% of people that take this test score between 2 15 and 8 15 So now that we've got our bell curve sorted out, we can go ahead and start answering our questions. So part A is asking for what percentage of students have an S A T mask or greater than 6 15 So 6 15 is I'm just going to go ahead and erase this here so that it doesn't get a too messy What? We're trying to do our math. So six fifteens right here and it wants the percentage of all the students scoring above that. That's 13% plus 2% plus a really, really tiny decimal over here. So you're about 15% of students. Two answers approximately 15 percent of students. Part B is asking what percentage of students have an s A T mask or greater than 7 15 So you'll do a similar thing. Except now, instead of from 6 15 you're going to look at from 7 15 So that's from here. So that's 2% plus some negligible percentage over here. So that's approximately 2% part C. What percentage of students have an S A T math score between 4 15 the one Oh, and 5 15 So between 4 15 and 5 15 Got a little excited. There. Hold on. There we go. So between 4 15 5 15 So between here and here Well, we already have that percentage written right here. So we already know that that's approximately 34% now. Obviously, it's not exactly 34%. Um, there's there's it's got its own errors and standard deviations going on in here. That's what I'm saying. Approximately. And then finally, part D. What percentage of students have an S a T mask or between 3 15 and 6 15 So just get rid of this. Make sure you don't race too much. So between 3 15 and 6 15 so we've got a 13% chunk here, a 34% chunk here and a 34% chunk here at those all together you end up with 81 percent. Well, say, approximately 81%.

All right, this question deals will test scores that are normally distributed with a mean and standard deviation scene here. So the first question asks, What percentage of students are scoring between 405 100 points? So we use normal CDF with our lower bound upper bound and the Mu and Sigma given to us at the start, and that turns out to be 38 point soon. 9% than Part B asks us if someone's scores a score of 6 30 What what percentage of people scored better, So that's normal. CDF of are lower bound 6 30 Our upper bound is a large number, and we still use the Mu and Sigma given to us, and that turns out to be 3.59% scored better. And from that, we know that 96.41% must have scored worse because we just do one minus 3.59 All right, See asks for the probability that a student scores above a 4 80 which is a normal CDF oh, for 80 large number New Sigma, and that equals 38.21%. So that's saying, if that's the cutoff score for a college, 38.21% of students are good enough for them

Mhm. For Scott We're dealing both with comparing him to his classmates and then to all juniors. So it tells us, first of all, that with his classmates, he scored at the 68th%,ile, meaning he beat 68% of his classmates, and then 32% of them beat him. In terms of the all. When we compare him to all the juniors, it tells, tells us that 5.2% of junior's scored above him, so that means he's gonna be at 100%, take away the 5.2% that scored above him, and that will land him at the 94 point eighth percentile. So when we look at these percentiles, he scored better when we look at all of the juniors rather than just his classmates. Now, in terms of calculator, in their Z scores, the Z score for these two populations, we should end up with the same kind of results. So for the juniors Scott, Z. Score, his observed value is 64, And then we're gonna subtract the mean, which for all the juniors was 46.9 And divided by their standard deviation, which was 10.9. And that gives us a Z score right around 1.57. So he scored a little over 1.5 standard deviations above the mean. When we compare him to everybody that took this test in the United States, Now, when we're just working with his classmates, his Z score is still his 64. The average from his classmates was 58 to With a standard deviation of 9.4. And when we calculate that, we get a Z score of .62. So again, his Z score was higher compared to all the juniors. So he scored better when we compare him to everybody rather than just his school.


Similar Solved Questions

5 answers
Pt) Evaluate the indefinite integral using integration by parts (twice) sin(3x) dx+C.(Note that the +C is already there for you; s0 dont add it in againl)
pt) Evaluate the indefinite integral using integration by parts (twice) sin(3x) dx +C. (Note that the +C is already there for you; s0 dont add it in againl)...
5 answers
80lgi Ciculate soilton collectcd > V 09 Soluuisr 5 1 1 2 AgNO;(aq) tests cor troarnach 250, combine wth the sllver chlarido AgCls) 3 VL brgheride 8 d amle *vt chicride precipitale iron(III) chloride; nich 1
8 0lgi Ciculate soilton collectcd > V 09 Soluuisr 5 1 1 2 AgNO;(aq) tests cor troarnach 250, combine wth the sllver chlarido AgCls) 3 VL brgheride 8 d amle *vt chicride precipitale iron(III) chloride; nich 1...
5 answers
Y(8) =3f(8) = 0,g(8) =-2,f "(-2)=10.g '(0)=5_ und Given f{8)=-1,8 f )(x) J() =(f og)x) K(x) find the following H()=(f 'gKr) G(r) =(8*- g(x)derivatives: #(S)G"(8](3) J"(8)8(4) K (x)
Y(8) =3f(8) = 0,g(8) =-2,f "(-2)=10.g '(0)=5_ und Given f{8)=-1,8 f )(x) J() =(f og)x) K(x) find the following H()=(f 'gKr) G(r) =(8*- g(x) derivatives: #(S) G"(8] (3) J"(8) 8(4) K (x)...
5 answers
[-/1 Points]DETAILSSERCPIT3.1.P,005.MY NOTESAsk YOUR TEACHERPRACTICE ANOTHERA cortravcling at 20. ms wncn huumns dur Gculh and accelerates veraar acccicration (n ms'27.5 Ms;curina5Dne Caleulateina magnituce of the crsMs?Need Help?FabanilWatch
[-/1 Points] DETAILS SERCPIT3.1.P,005. MY NOTES Ask YOUR TEACHER PRACTICE ANOTHER A cor travcling at 20. ms wncn huumns dur Gculh and accelerates veraar acccicration (n ms' 27.5 Ms; curina 5Dne Caleulateina magnituce of the crs Ms? Need Help? Fabanil Watch...
5 answers
3. Hemiacetal formation between (structures only, no names)Butanal and 1-butanolCyclohexanone and butanol4 Ester formation betweenButanoic acid and butanolButanoic acid and cyclohexanol
3. Hemiacetal formation between (structures only, no names) Butanal and 1-butanol Cyclohexanone and butanol 4 Ester formation between Butanoic acid and butanol Butanoic acid and cyclohexanol...
5 answers
Tat J Common 10, Final Spring 0-3-6 Points) A local ) 2019 to them by the health center local bospital: noted that in- sample of 400 Paticnts 80 Were refetred Provide a 95%= confidenceF center by the interval for all the paticnts who are referred to the health hospital.proponion of hospital referrals Aould be required t0 cstimate the What size sample 959 confidence? margin of e cmor of 0.04 or Iess at with
tat J Common 10, Final Spring 0-3-6 Points) A local ) 2019 to them by the health center local bospital: noted that in- sample of 400 Paticnts 80 Were refetred Provide a 95%= confidenceF center by the interval for all the paticnts who are referred to the health hospital. proponion of hospital referr...
5 answers
Which is a neutralization reaction?Select the correct answer below:HCIaq)+NaOHaq) ~NaCllaq)+H2O()Clzlaq)+HzO() HCI(aq)+OH-(aq)CaClz(aq) Ca2t(aq)+2CI-(aq)HCl(aq)+H2O ()_ ~H3O+(aq)+CI-(aq)
Which is a neutralization reaction? Select the correct answer below: HCIaq)+NaOHaq) ~NaCllaq)+H2O() Clzlaq)+HzO() HCI(aq)+OH-(aq) CaClz(aq) Ca2t(aq)+2CI-(aq) HCl(aq)+H2O ()_ ~H3O+(aq)+CI-(aq)...
5 answers
Using Lagrange multipliers, find the point on the plane x + 3y + 3z = that is closest to the origin_Enter the exact answers as improper fractions, if necessary:(x,y,z) =EditEditEdit
Using Lagrange multipliers, find the point on the plane x + 3y + 3z = that is closest to the origin_ Enter the exact answers as improper fractions, if necessary: (x,y,z) = Edit Edit Edit...
5 answers
Why is a many-step cyclic process more efficient in utilizing energy from food than a single-step combustion?
Why is a many-step cyclic process more efficient in utilizing energy from food than a single-step combustion?...
5 answers
V(X) = 4.Find 6(9 random variable X has Discrete A. 42X)0 B. V970 C. -4D. -16E: V6sReset Selection
V(X) = 4.Find 6(9 random variable X has Discrete A. 4 2X) 0 B. V97 0 C. -4 D. -16 E: V6s Reset Selection...
5 answers
Question 6 (4 + 4 points) Consider the integral 591 5+1y dyds Sketch the region of integration 6) Reverse the order of integration DO NOT EVALUATE THE INTEGRALI
Question 6 (4 + 4 points) Consider the integral 591 5+1y dyds Sketch the region of integration 6) Reverse the order of integration DO NOT EVALUATE THE INTEGRALI...
5 answers
A ball of 100 g is thrown from the window with a speed of 8 m/sand an angle of 30° up from the horizontal. Use the law ofconservation of energy.Q.(1)Get the kinetic energy of the ball from the top of the flighttrack.(2) Find the speed at which the ball is 3 meters below thewindow.
A ball of 100 g is thrown from the window with a speed of 8 m/s and an angle of 30° up from the horizontal. Use the law of conservation of energy. Q. (1)Get the kinetic energy of the ball from the top of the flight track. (2) Find the speed at which the ball is 3 meters below the window....
5 answers
For iron_ Fe, the heat of fusion at its normal melting point 0f 1535 cC is 16.2 kJmol.The = entropy change when 2.37 moles of solid Fe melts at 1535 "C, alm"21.236 WKAn error has been detected your answer. Check for typos miscalculations ctc: before submitting your answer.
For iron_ Fe, the heat of fusion at its normal melting point 0f 1535 cC is 16.2 kJmol. The = entropy change when 2.37 moles of solid Fe melts at 1535 "C, alm "21.236 WK An error has been detected your answer. Check for typos miscalculations ctc: before submitting your answer....
5 answers
QUESTION 17from conception t0 birth varies according t0 distribution that is The length of human pregnancies mean M = 266 days and standard deviation 0 = 16 days_ approximately Normal with WJS considered the g5th percentile? How many days would pregnancy last Round your answer t0 the nearest doy;
QUESTION 17 from conception t0 birth varies according t0 distribution that is The length of human pregnancies mean M = 266 days and standard deviation 0 = 16 days_ approximately Normal with WJS considered the g5th percentile? How many days would pregnancy last Round your answer t0 the nearest doy;...

-- 0.025286--