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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.
|
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 |
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