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Probability problem, central limit theorm/binomial

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    if a student writes a true-false test and guesses each answer, what is the probability that he can get 120 to 140 correct answers if there are 200 questions on the test?


    2. Relevant equations
    central limit theorm and binomial distribution
    my teacher game me a chart that gives area under a normal curve for given z-values ranging from 3.4 to -3.4


    3. The attempt at a solution
    what i have so far is: n= 200 np(mean)= (0.5)(200)= 100 standard deviation= sqrt(0.5)(0.5)(200)= 7.07
    since the question wants the probability between 120 and 140 (im guessing this is inclusive, the question doesnt specify) i have:
    P(120<=x<=140)
    = P(119.5<x<140.5)
    = 119.5-100/7.07(sqrt200)<x<140.5-100/7.07(sqrt200)
    after the calculation i get:
    0.1950<z<0.4051

    now, i know i go to my table and get the areas under the curves for those two numbers, but what do i do next dince i have the two numbers? do i subtract them?
     
  2. jcsd
  3. Feb 25, 2009 #2
    The normal distribution table may give you numbers of P(Z < z), -inf to z. I think that you need to find P(.195 < Z < .4051), that would be P(Z < .4051) - P(Z < .195).
     
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