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