Find the probability that the student gets exactly 15 correct answers.

Mathematics
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A student answers all 48 questions on a multiple choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to approximate the binomial distribution. 

May 1st, 2015

Find the mean:

Mean = np

          = 48*(1/4)

           = 12

Find the standard deviation:
SD = sqrt(npq)

      = sqrt(48 *1/4 *3/4)

      = 3
"15" means 14.5 to 15.5
z1= (14.5-12)/3 = 0.833

z2 = (15.5-12)/3 = 1.167

From normal distribution table

P(0.833 < z < 1.167) = 0.0808

May 1st, 2015

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