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California Exit Test

If 100,000 California students just guessed on an examination which included 40 questions with four multiple choice answers, they would each get an average of 10 questions correct, for an average of 25,000 students with correct guesses.  If the distribution of the scores is a bell curve, then 18,750 of them would get 10 questions correct, 2,344 would get between 2.5 to 10 answers correct and another 2,344 would get between 10 to 17.5 answers correct.  586 would get between .6 and 2.5 answers correct and another 586 would get between 17.5 to 19.4 answers correct.  146 would get between .2 to .6 answers correct and another 146 would get between 19.4 to 19.8 answers correct.  With the small sample size of only 100,000 students, 12 of them would be expected to get more  than 20 answers correct, and 12 would be expected to get none of them correct.

califexittest1.gif (36167 bytes)

 

Prob of wrong answer

Prob of right answer

Odds of wrong answer

Odds of Right Answer

Percent of all correct proba bilities

Percent of all wrong proba bilities

Number of students correct

Number of students wrong

Distr Students with correct answers

Percent Correct Answers

Number Correct Answers

1

0.75000

0.25000000000000000000

1

4

75.00%

25.004%

18,750.0

75,000.0

40

2

0.56250

0.06250000000000000000

2

16

18.75%

18.753%

4,687.5

15,002.7

3

0.42188

0.01562500000000000000

2

64

4.69%

14.065%

1,171.9

11,252.0

4

0.31641

0.00390625000000000000

3

256

1.17%

10.549%

293.0

8,439.0

5

0.23730

0.00097656250000000000

4

1,024

0.29%

7.912%

73.2

6,329.3

6

0.17798

0.00024414062500000000

6

4,096

0.07%

5.934%

18.3

4,746.9

7

0.13348

0.00006103515625000000

7

16,384

0.02%

4.450%

4.6

3,560.2

8

0.10011

0.00001525878906250000

10

65,536

0.00%

3.338%

1.1

2,670.2

9

0.07508

0.00000381469726562500

13

262,144

0.00%

2.503%

0.3

2,002.6

10

0.05631

0.00000095367431640625

18

1,048,576

0.00%

1.877%

0.1

1,502.0

11

0.04224

0.00000023841857910156

24

4,194,304

0.00%

1.408%

0.0

1,126.5

0

50.0%

20.0

12

0.03168

0.00000005960464477539

32

16,777,216

0.00%

1.056%

0.0

844.9

1

50.0%

20.0

13

0.02376

0.00000001490116119385

42

67,108,864

0.00%

0.792%

0.0

633.6

2

50.0%

20.0

14

0.01782

0.00000000372529029846

56

268,435,456

0.00%

0.594%

0.0

475.2

9

49.98%

20.0

15

0.01336

0.00000000093132257462

75

1,073,741,824

0.00%

0.446%

0.0

356.4

37

49.90%

20.0

16

0.01002

0.00000000023283064365

100

4,294,967,296

0.00%

0.334%

0.0

267.3

146

49.61%

19.8

17

0.00752

0.00000000005820766091

133

17,179,869,184

0.00%

0.251%

0.0

200.5

586

48.44%

19.4

18

0.00564

0.00000000001455191523

177

68,719,476,736

0.00%

0.188%

0.0

150.4

2,344

43.75%

17.5

19

0.00423

0.00000000000363797881

237

274,877,906,944

0.00%

0.141%

0.0

112.8

18,750

25.0%

10.0

20

0.00317

0.00000000000090949470

315

1,099,511,627,776

0.00%

0.106%

0.0

84.6

2,344

6.3%

2.5

21

0.00238

0.00000000000022737368

420

4,398,046,511,104

0.00%

0.079%

0.0

63.4

586

1.6%

0.6

22

0.00178

0.00000000000005684342

561

17,592,186,044,416

0.00%

0.059%

0.0

47.6

146

0.4%

0.2

23

0.00134

0.00000000000001421085

747

70,368,744,177,664

0.00%

0.045%

0.0

35.7

37

0.1%

0.0

24

0.00100

0.00000000000000355271

997

281,474,976,710,656

0.00%

0.033%

0.0

26.8

9

0.0%

0.0

25

0.00075

0.00000000000000088818

1,329

1,125,899,906,842,620

0.00%

0.025%

0.0

20.1

2

0.0%

0.0

26

0.00056

0.00000000000000022204

1,772

4,503,599,627,370,500

0.00%

0.019%

0.0

15.1

1

0.0%

0.0

27

0.00042

0.00000000000000005551

2,362

18,014,398,509,482,000

0.00%

0.014%

0.0

11.3

0

0.0%

0.0

28

0.00032

0.00000000000000001388

3,150

72,057,594,037,927,900

0.00%

0.011%

0.0

8.5

0

29

0.00024

0.00000000000000000347

4,200

288,230,376,151,712,000

0.00%

0.008%

0.0

6.4

30

0.00018

0.00000000000000000087

5,600

1,152,921,504,606,850,000

0.00%

0.006%

0.0

4.8

 

califexittest2.gif (36994 bytes)

 

califexittest3.gif (35938 bytes)