Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.For the SAT critical reading score, the mean was 501 with a standard deviation of 112.For the SAT mathematics score, the mean was 516 with a standard deviation of 116.Fill in the blanks of the following sentences. An ACT composite score of 32 is at the ________th percentile. ________% of the scores are lower than 32. An SAT critical reading score of 780 is at the ________th percentile. ________% of the scores are lower than 780. An SAT mathematics score of 760 is at the ________th percentile. ________% of the scores are lower than 760. Z-Tablez 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09-3.40.0003 0.0003 0.00030.00030.0003 0.0003 0.0003 0.0003 0.00030.0002-3.30.0005 0.0005 0.00050.00040.00040.0004 0.0004 0.00040.0004 0.0003-3.20.00070.00070.00060.00060.00060.0006 0.00060.00050.0005 0.0005-3.10.00100.00090.00090.00090.00080.0008 0.0008 0.00080.00070.0007-3.00.00130.00130.00130.00120.00120.00110.00110.00110.00100.0010-2.90.00190.0018 0.0018 0.00170.00160.0016 0.00150.00150.00140.0014-2.80.00260.00250.00240.00230.0023 0.0022 0.00210.00210.00200.0019-2.70.00350.00340.00330.00320.00310.00300.00290.00280.00270.0026-2.60.00470.00450.00440.00430.0041 0.00400.00390.00380.00370.0036-2.50.00620.00600.00590.00570.0055 0.00540.0052 0.00510.00490.0048-2.40.00820.00800.00780.00750.00730.00710.00690.00680.00660.0064-2.30.01070.0104 0.01020.00990.00960.0094 0.0091 0.00890.00870.0084-2.20.0139 0.01360.0132 0.01290.0125 0.01220.01190.01160.01130.0110-2.10.01790.01740.01700.01660.01620.01580.01540.01500.01460.0143-2.00.02280.02220.02170.02120.02070.02020.01970.01920.01880.0183-1.90.02870.02810.02740.0268 0.02620.0256 0.02500.02440.02390.0233-1.80.03590.03510.03440.03360.03290.03220.03140.03070.03010.0294-1.70.04460.04360.04270.04180.04090.04010.0392 0.03840.03750.0367-1.60.05480.05370.05260.05160.05050.0495 0.04850.04750.04650.0455-1.50.06680.0655 0.06430.06300.06180.06060.0594 0.05820.05710.0559-1.40.08080.07930.07780.07640.07490.07350.07210.07080.06940.0681-1.30.09680.09510.09340.09180.09010.08850.08690.08530.08380.0823-1.20.11510.11310.11120.10930.10750.10560.10380.10200.10030.0985-1.10.13570.13350.13140.12920.12710.1251 0.1230 0.12100.11900.1170-1.00.15870.15620.15390.15150.14920.14690.14460.14230.14010.1379-0.90.18410.18140.17880.17620.17360.17110.1685 0.16600.16350.1611-0.80.21190.2090 0.20610.20330.20050.1977 0.19490.19220.18940.1867-0.70.24200.23890.23580.23270.22960.22660.22360.22060.21770.2148-0.60.27430.27090.26760.26430.26110.25780.25460.25140.24830.2451-0.50.30850.30500.30150.29810.29460.29120.28770.28430.28100.2776-0.40.34460.34090.33720.33360.33000.32640.32280.31920.31560.3121-0.30.38210.37830.37450.37070.36690.36320.35940.35570.35200.3483-0.20.42070.41680.41290.40900.40520.40130.39740.39360.38970.3859-0.10.46020.45620.45220.44830.44430.44040.43640.43250.42860.42470.0 0.50000.49600.49200.48800.48400.4801 0.47610.47210.46810.4641 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.50000.50400.50800.51200.51600.51990.52390.52790.53190.53590.1 0.5398 0.5438 0.54780.55170.55570.55960.56360.56750.57140.57530.2 0.57930.58320.58710.59100.59480.59870.60260.60640.61030.61410.3 0.61790.62170.62550.62930.63310.63680.64060.64430.64800.65170.4 0.65540.65910.66280.66640.67000.67360.67720.68080.68440.68790.5 0.69150.69500.69850.70190.70540.70880.71230.71570.71900.72240.6 0.7257 0.72910.73240.73570.73890.7422 0.74540.74860.75170.75490.7 0.75800.76110.76420.76730.77040.77340.77640.77940.78230.78520.8 0.78810.79100.79390.79670.79950.80230.80510.80780.81060.81330.9 0.81590.81860.82120.82380.82640.82890.83150.83400.83650.83891.0 0.84130.84380.84610.84850.85080.85310.85540.85770.85990.86211.1 0.86430.86650.86860.87080.87290.87490.87700.87900.88100.88301.2 0.88490.88690.88880.89070.89250.89440.89620.89800.89970.90151.3 0.90320.90490.90660.90820.90990.91150.91310.91470.91620.91771.4 0.91920.92070.92220.92360.92510.92650.92790.92920.93060.93191.5 0.93320.93450.93570.93700.93820.93940.94060.94180.94290.94411.6 0.94520.94630.94740.94840.94950.95050.95150.95250.95350.95451.7 0.95540.95640.95730.95820.95910.95990.96080.96160.96250.96331.8 0.96410.96490.96560.96640.96710.96780.96860.96930.96990.97061.9 0.97130.97190.97260.97320.97380.97440.97500.97560.97610.97672.0 0.97720.97780.97830.97880.97930.97980.98030.98080.98120.98172.1 0.98210.9826 0.98300.98340.98380.98420.98460.98500.98540.98572.2 0.98610.98640.98680.98710.98750.98780.98810.98840.98870.98902.3 0.9893 0.98960.98980.99010.99040.99060.99090.99110.99130.99162.4 0.99180.99200.99220.99250.99270.99290.99310.99320.99340.99362.5 0.9938 0.99400.99410.99430.99450.99460.99480.99490.99510.99522.6 0.99530.99550.99560.99570.99590.99600.99610.99620.99630.99642.7 0.99650.99660.99670.99680.99690.99700.99710.99720.99730.99742.8 0.99740.99750.99760.99770.99770.9978 0.99790.9979l0.99800.99812.9 0.99810.99820.99820.99830.99840.99840.99850.99850.99860.99863.0 0.99870.99870.99870.99880.99880.99890.99890.99890.99900.99903.1 0.99900.9991 0.99910.99910.99920.99920.99920.99920.99930.99933.2 0.99930.99930.99940.99940.99940.99940.99940.99950.99950.99953.3 0.99950.99950.99950.99960.99960.9996 0.99960.99960.99960.99973.4 0.9997 0.9997 0.9997 0.99970.99970.9997 0.9997 0.99970.9997 0.9998

here use basic of Normal distribution

Answered: An ACT composite score of 32 is at the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Many students take standardized tests for college applications. They are called standardized tests because they are scored so the population of student scores for any one particular test follows a normal distribution. The most common test are the SAT and the ACT.

Suppose the mean and standard deviation for the ACT composite score, the SAT critical reading score, and the SAT mathematics score for the year 2017 are as follows:

For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.
For the SAT critical reading score, the mean was 501 with a standard deviation of 112.
For the SAT mathematics score, the mean was 516 with a standard deviation of 116.

Fill in the blanks of the following sentences.

An ACT composite score of 32 is at the ________th percentile. ________% of the scores are lower than 32.

An SAT critical reading score of 780 is at the ________th percentile. ________% of the scores are lower than 780.

An SAT mathematics score of 760 is at the ________th percentile. ________% of the scores are lower than 760.

Z-Table
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.40.0003 0.0003 0.00030.00030.0003 0.0003 0.0003 0.0003 0.00030.0002
-3.30.0005 0.0005 0.00050.00040.00040.0004 0.0004 0.00040.0004 0.0003
-3.20.00070.00070.00060.00060.00060.0006 0.00060.00050.0005 0.0005
-3.10.00100.00090.00090.00090.00080.0008 0.0008 0.00080.00070.0007
-3.00.00130.00130.00130.00120.00120.00110.00110.00110.00100.0010
-2.90.00190.0018 0.0018 0.00170.00160.0016 0.00150.00150.00140.0014
-2.80.00260.00250.00240.00230.0023 0.0022 0.00210.00210.00200.0019
-2.70.00350.00340.00330.00320.00310.00300.00290.00280.00270.0026
-2.60.00470.00450.00440.00430.0041 0.00400.00390.00380.00370.0036
-2.50.00620.00600.00590.00570.0055 0.00540.0052 0.00510.00490.0048
-2.40.00820.00800.00780.00750.00730.00710.00690.00680.00660.0064
-2.30.01070.0104 0.01020.00990.00960.0094 0.0091 0.00890.00870.0084
-2.20.0139 0.01360.0132 0.01290.0125 0.01220.01190.01160.01130.0110
-2.10.01790.01740.01700.01660.01620.01580.01540.01500.01460.0143
-2.00.02280.02220.02170.02120.02070.02020.01970.01920.01880.0183
-1.90.02870.02810.02740.0268 0.02620.0256 0.02500.02440.02390.0233
-1.80.03590.03510.03440.03360.03290.03220.03140.03070.03010.0294
-1.70.04460.04360.04270.04180.04090.04010.0392 0.03840.03750.0367
-1.60.05480.05370.05260.05160.05050.0495 0.04850.04750.04650.0455
-1.50.06680.0655 0.06430.06300.06180.06060.0594 0.05820.05710.0559
-1.40.08080.07930.07780.07640.07490.07350.07210.07080.06940.0681
-1.30.09680.09510.09340.09180.09010.08850.08690.08530.08380.0823
-1.20.11510.11310.11120.10930.10750.10560.10380.10200.10030.0985
-1.10.13570.13350.13140.12920.12710.1251 0.1230 0.12100.11900.1170
-1.00.15870.15620.15390.15150.14920.14690.14460.14230.14010.1379
-0.90.18410.18140.17880.17620.17360.17110.1685 0.16600.16350.1611
-0.80.21190.2090 0.20610.20330.20050.1977 0.19490.19220.18940.1867
-0.70.24200.23890.23580.23270.22960.22660.22360.22060.21770.2148
-0.60.27430.27090.26760.26430.26110.25780.25460.25140.24830.2451
-0.50.30850.30500.30150.29810.29460.29120.28770.28430.28100.2776
-0.40.34460.34090.33720.33360.33000.32640.32280.31920.31560.3121
-0.30.38210.37830.37450.37070.36690.36320.35940.35570.35200.3483
-0.20.42070.41680.41290.40900.40520.40130.39740.39360.38970.3859
-0.10.46020.45620.45220.44830.44430.44040.43640.43250.42860.4247
0.0 0.50000.49600.49200.48800.48400.4801 0.47610.47210.46810.4641

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359
0.1 0.5398 0.5438 0.54780.55170.55570.55960.56360.56750.57140.5753
0.2 0.57930.58320.58710.59100.59480.59870.60260.60640.61030.6141
0.3 0.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517
0.4 0.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879
0.5 0.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224
0.6 0.7257 0.72910.73240.73570.73890.7422 0.74540.74860.75170.7549
0.7 0.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852
0.8 0.78810.79100.79390.79670.79950.80230.80510.80780.81060.8133
0.9 0.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389
1.0 0.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621
1.1 0.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830
1.2 0.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015
1.3 0.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177
1.4 0.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319
1.5 0.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441
1.6 0.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545
1.7 0.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633
1.8 0.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706
1.9 0.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767
2.0 0.97720.97780.97830.97880.97930.97980.98030.98080.98120.9817
2.1 0.98210.9826 0.98300.98340.98380.98420.98460.98500.98540.9857
2.2 0.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890
2.3 0.9893 0.98960.98980.99010.99040.99060.99090.99110.99130.9916
2.4 0.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936
2.5 0.9938 0.99400.99410.99430.99450.99460.99480.99490.99510.9952
2.6 0.99530.99550.99560.99570.99590.99600.99610.99620.99630.9964
2.7 0.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974
2.8 0.99740.99750.99760.99770.99770.9978 0.99790.9979l0.99800.9981
2.9 0.99810.99820.99820.99830.99840.99840.99850.99850.99860.9986
3.0 0.99870.99870.99870.99880.99880.99890.99890.99890.99900.9990
3.1 0.99900.9991 0.99910.99910.99920.99920.99920.99920.99930.9993
3.2 0.99930.99930.99940.99940.99940.99940.99940.99950.99950.9995
3.3 0.99950.99950.99950.99960.99960.9996 0.99960.99960.99960.9997
3.4 0.9997 0.9997 0.9997 0.99970.99970.9997 0.9997 0.99970.9997 0.9998

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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