On a certain quiz with 25 questions, each correct answer is scored 4 points and each incorrect answer is scored –1 point. questions not answered receive no points. a student who answered 23 questions and had a total score of 82 points answered how many questions correctly? 18 19 20 21 22

x correct answers

23 - x incorrect answers

82 = 4x + -1(23 - x) = 3x - 23

105 = 5 x

x = 105/5 = 21

21 right 2 wrong 2 unanswered

Check: 4(21) -1(2) = 84-2=82 good

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

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