Binomial Distribution Examples

Please do the following examples sequentially.

Example One

EXPERIMENT: One person (N = 1) takes a twenty question (n = 20) true-false examination by guessing on every question.

Every time the "EXECUTE THE EXPERIMENT ONCE" button is selected (or the "return" key is pressed), the applet simulates one person taking the test. The number of questions guessed correctly is displayed. Notice that the bar tends to "pop-up" most frequently around ten.

Example Two

EXPERIMENT: One-hundred people (N = 100) each take a twenty question (n = 20) true-false examination by guessing on every question.

Every time the "EXECUTE THE EXPERIMENT ONCE" button is selected (or the "return" key is pressed), the applet simulates one hundred people taking the test. The number of people who score 0/20, 1/20 ... 20/20 is displayed.

10/20 is a pass. Place the cursor in the bar representing n = 10 and "click" the mouse button to see that N(score=10)=18. If 100 people guess on every question of a twenty question true-false test, the theoretical number or people who will get exactly ten correct out of twenty is 18.

Place the cursor in the bar representing n = 10 and "click and drag" the cursor to the right, slightly past twenty (on the horizontal n-axis) to see that N(score>9)=58. If 100 people guess on every question of a twenty question true-false test, the theoretical number of people who will pass is 58.

Example Three

EXPERIMENT: One-hundred people (N = 100) each take a twenty question (n = 20) four choice per question multiple choice examination by guessing on every question. Only one choice is correct per question.

Place the cursor in the bar representing n = 10 and "click and drag" the cursor to the right, slightly past twenty (on the horizontal n-axis) to see that N(score>9)=1. If 100 people guess on every question of a twenty question multiple choice test, the theoretical number or people who will pass is 1.

Look at the distribution of values to see that the binomial distribution of values representing the possible outcomes can be approximated by a normal curve with a mean of 5 (np = 100 × 0.25) and a standard deviation of approximately 1.94 [standard deviation = the square root of (npq)].


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