4

Problem-14 A Six- ~Sigma Black Belt is studying the performance of financial analysts from a bank using their scores on a certain aptitude test She has collected d...

Question

Problem-14 A Six- ~Sigma Black Belt is studying the performance of financial analysts from a bank using their scores on a certain aptitude test She has collected data on a random sample lof 52 analysts with an average of 85 and standard deviation of 4.2, Find a 90% Cl for the average score of all analysts from this bank b) Find a 90% Cl on the standard deviation of the scores

Problem-14 A Six- ~Sigma Black Belt is studying the performance of financial analysts from a bank using their scores on a certain aptitude test She has collected data on a random sample lof 52 analysts with an average of 85 and standard deviation of 4.2, Find a 90% Cl for the average score of all analysts from this bank b) Find a 90% Cl on the standard deviation of the scores



Answers

A population has mean 72 and standard deviation 6 . a. Find the mean and standard deviation of $x-$ for samples of size $45 .$ b. Find the probability that the mean of a sample of size 45 will differ from the population mean 72 by at least 2 units, that is, is either less than 70 or more than 74 .

For this problem, we're going to start by finding our cumulative relative frequency distribution. Um, we already found the relative frequency distribution in the previous question, So I already copied that information down, and we're just going to fill in the cumulative relative frequency column. So to get the cumulative relative frequency for the class 0 to 4, it's the same as the relative frequency, which is 40.8 for the Class four through eight. We add the previous cumulative relative frequency of 80.8 to the classes relative frequency 0.16 So that's going to give us 0.24 and we continue to add the previous cumulative relative frequency to the new classes relative frequency. So for eight through 12 we're going to do point to four plus 40.16 which is going to give us 0.40 for 12 through 16. We're gonna do 160.40 plus 0.40 which would give us 0.80 for 16 through 20. We do 200.80 plus 0.1 to which gives this 0.92 for 23 24. We do 240.92 plus point of six, which gives this 60.98 and last class 24 through 28 we add 280.98 and 0.2 which gives us 1.0. Now, we're gonna use this cumulative relative frequency distribution to construct our dog. I've and part B. Now we're going to construct are all guys. So we start by labeling the X and Y axis. The X axis is test scores and we use the class boundaries. And then the cumulative relative frequency goes on the Y axis. And of course, we've titled our graph at the top. So now, to create our archive for each class, remember that the cumulative relative frequency is plotted at the upper boundary of each class. So for the cause, 0 to 4, we start at 00 and then we plot the cumulative relative frequency of 0.0 a at the four. And then we connect those with a wine for the class four through eight. We plot the key months of relative frequency of 0.24 at the A because that's the upper class boundary, and we again connect with a line. So then, at 12 we plot the 120.40 connect with the line at 16 we plot 160.80 at 20. Re plot the 200.92 At 24 we plot the 240.98 and at 28 we get to 1.0. Where are five should end and that is the AWG I for our data. Now we're going to use our archive to answer part C. So for part C, we are going to look for what percent have no more than 16. So we go to 16 on our archive and we're gonna go up to the line from there, and then we're going to go over and see what the value is. And we know when we constructed the AWG, I've at 16 we plotted a cumulative relative frequency of 160.80 But one thing to keep in mind is that that 10.80 doesn't include the value 16. And when we talk about no more than 16 16 is included. So we're thinking with no more than 16 you're thinking less than or equal to 16. And so that percentage right there, 80% doesn't really include he 16 necessarily. But it's a good approximation, so we can say that approximately 80% of students scored no more than 16

In this question were given a mean and sample standard deviation for some test scores and asked to find the Z scores for several individual data values. So let's say we have the mean of 74.2 on a sample standard deviation of 11.5. If you recall the formula for finding a Z score is X minus X bar over s where X is the data value. X bar is the sample mean and s is the sample standard deviation. So for our first part of the question, we are given us test score of 54. So somebody who performed pretty well below average So to find there's you score will substitute all of our known information into the formula for the Z score and divide by our standard deviation. So subtraction first, following order of operations and then division gives us a Z score of negative 1.76 So somebody who scored between one and two standard deviations below the mean Our second test score is 68. So somebody who scored below the mean but not as far below the mean, so we would expect disease score below zero, but not as far below zero. So 68 minus 74.2 over 11.5. And we find that that Z score is in fact negative. But on Lee negative 0.54. What if somebody performs better than average? So what if somebody got a test score of 79 so a little bit above average. So we would again substitute all of our known information into the formula and divide by our standard deviation here. And we're going to expect a Z score above zero, but not a lot above zero, because this score is not very far above average. So that's a Z score of 0.42 and then finally parte de what if somebody did even better above average? What if they scored in 93? So we would expect again a positive Z score because the scores above average, but it's even further above average. So even higher number and this ups supposed to be a five, not a 11.2 11.5, and this sea score turns out to be 1.63

So in this question, we're told that scores in an exam are normally distributed with me 382 and standard deviation 26, And we're justifying the score that is in the 50th%ile. So that's basically this score right here, 58%ile, so that C0 point Hi, so probably that Z is less than the star is point five, So these are in our case is zero. And so that translates to a score x star of 382 45. Okay, for being with us to find the score that's in the 90th percentile, So that's followed easy, less than Z Star is equal to not 0.9. And for that our value of Z star is 1.28, which converts to an ext r value of 415 work part.


Similar Solved Questions

5 answers
How many 'H NMR signals does each compound give? [4 points]How many 'IC NMR signals does each compound exhibit? [4 points]The following molecules are constitutional isomers of between the two using 'H NMR: [6 points] each other: How could you distinguish
How many 'H NMR signals does each compound give? [4 points] How many 'IC NMR signals does each compound exhibit? [4 points] The following molecules are constitutional isomers of between the two using 'H NMR: [6 points] each other: How could you distinguish...
5 answers
% COMP OF MEDIUMX100% COMP OF POPULATIONCPMMeta Cst X100o IMPRESSIONSX10001% OF TARGET UNIVERSE
% COMP OF MEDIUM X100 % COMP OF POPULATION CPM Meta Cst X100o IMPRESSIONS X1000 1% OF TARGET UNIVERSE...
5 answers
Q3-Predict the geometry of the following ions:INH 21C0;3)H,0
Q3-Predict the geometry of the following ions: INH 21C0; 3)H,0...
5 answers
N4s ii 0,(e} n3nt 0' [07828 E1244412
N4s ii 0, (e} n3nt 0' [07828 E1244412...
5 answers
Use a solids of revolution method to do #15_15) The solid formed by revolving (about the X-axis) the unbounded region lying between the graph of f (x) = and the X-axis (x > 1) is called Gabriel's Horn. Show that this solid has finite volume and an infinite surface area__
Use a solids of revolution method to do #15_ 15) The solid formed by revolving (about the X-axis) the unbounded region lying between the graph of f (x) = and the X-axis (x > 1) is called Gabriel's Horn. Show that this solid has finite volume and an infinite surface area__...
5 answers
17. Wtite each expression as the product of two trigonometric functions: sin 30 Sin - 5018. Verify the identity:=-tan I sec I sin I + 1Sin I19. Solve for x:tan2 tan I - 3 = 020. Use power-reducing identities to verify:cos 41sin? r cOS? I =
17. Wtite each expression as the product of two trigonometric functions: sin 30 Sin - 50 18. Verify the identity: =-tan I sec I sin I + 1 Sin I 19. Solve for x: tan 2 tan I - 3 = 0 20. Use power-reducing identities to verify: cos 41 sin? r cOS? I =...
5 answers
6.2.77-BE ULateLut"el4eTluina aArareneDle07450]" T0casVetaamCnauuiren 41Vund9 dl equecnm6{38 culjan MuTen #71e67"0
6.2.77-BE ULate Lut"el4e Tluina aAraren eDle07 450]" T0cas Vetaam Cnauuiren 4 1Vund9 dl equecnm6{38 culjan MuTen #71e67"0...
1 answers
Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. $$y=x^{2}, \quad y=x^{2}-2$$
Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. $$y=x^{2}, \quad y=x^{2}-2$$...
5 answers
The time it takes me to wash the dishes is uniformly distributed between 12 minutes and minutes_What is the probability that washing dishes tonight will take me between 15 and 17 minutes?Give your answer accurate to two decimal places:
The time it takes me to wash the dishes is uniformly distributed between 12 minutes and minutes_ What is the probability that washing dishes tonight will take me between 15 and 17 minutes? Give your answer accurate to two decimal places:...
5 answers
Find - donain ( of Iie Function azd identify any Verucal aad IBonzoubl aycrdaT+4 fl) = I-16The domainreal numbets X exceplx = Mhcfe D 4 Vert l Lyn3i(e 4424 4lalretepti-_l Tkeuatstioil npr41e-k sdik The domamn all real numbersEeelnexcepil= Tlete is tertct munko The domain is all Teal "116 "Teara E ! (EEc Erepl [ domain is all real qunbes 0 The ~Ibar 5{a e nlnkn cep} = donun DsJ 0 The'Guard" NserActsau
Find - donain ( of Iie Function azd identify any Verucal aad IBonzoubl aycrda T+4 fl) = I-16 The domain real numbets X exceplx = Mhcfe D 4 Vert l Lyn3i(e 4424 4lal retepti-_l Tkeuatstioil npr41e-k sdik The domamn all real numbers Eeeln excepil= Tlete is tertct munko The domain is all Teal "116 ...
5 answers
Find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root.$$4 x^{4}-x^{3}+5 x^{2}-2 x-6=0$$
Find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. $$4 x^{4}-x^{3}+5 x^...
5 answers
Dndersine the Jui4O H on the ne recncon 1 H resultant force acting 1 resultant force acting E 1 Olesut m 1 Jno * punod # {88 125 fobjec; magnitude of the = '0,2 1 17 1will e particle w H 1 direction in 2 180 02 forces Detemine L TwoW~is 4 units is 4 units E. 1 Ic $ 0 three J} combinationHolal iaeenlc 0mnoxhe dnhcMit 1 1 (the
Dndersine the Jui4O H on the ne recncon 1 H resultant force acting 1 resultant force acting E 1 Olesut m 1 Jno * punod # {88 125 fobjec; magnitude of the = '0,2 1 17 1 will e particle w H 1 direction in 2 180 02 forces Detemine L Two W ~is 4 units is 4 units E. 1 Ic $ 0 three J} combination Hol...
5 answers
Can dimensional analysis (looking at the units) help you match which of these formulas-- ????r2 and 2????r -- goes with which of the following quantities: area of a circle and circumference of a circle? Explain.
Can dimensional analysis (looking at the units) help you match which of these formulas-- ????r2 and 2????r -- goes with which of the following quantities: area of a circle and circumference of a circle? Explain....
5 answers
Given the following chemical equation; how many grams of 02 are needed to form 13.25 g of Feo? 2Fe 02 + 2 Feo
Given the following chemical equation; how many grams of 02 are needed to form 13.25 g of Feo? 2Fe 02 + 2 Feo...
5 answers
Tne fia403 Delow (not t0 scale}. Yet L 1.200 [60 mmand 452ume cne [email protected] ~tecnCalculete the phase @ fference Detween the [ 0 wave fronts #miving & Knen500?Calculete tne phaze @utterence Dec ben [7Aaerrono ernvlcaKhen00 Mm;WWnet Ete Valut 08 for wnich tha phare difference 0,J3J tad7WuteMnc VEALtfor which tne Pata oimarence 154 /AnedSiada
tne fia403 Delow (not t0 scale}. Yet L 1.20 0 [60 mmand 452ume cne Weeystom Mminantd [email protected] Vicwing ~tecn Calculete the phase @ fference Detween the [ 0 wave fronts #miving & Knen 500? Calculete tne phaze @utterence Dec ben [7 Aaerrono ernvlca Khen 00 Mm; WWnet Ete Valut 08 for wnich tha...
4 answers
If z = sin(x + sin t) , show that dz 022 az 022 dx dxdt ax?
If z = sin(x + sin t) , show that dz 022 az 022 dx dxdt ax?...

-- 0.018649--