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ludmilkaskok [199]
3 years ago
10

A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of w

hich is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to approximate the binomial distribution.
Mathematics
1 answer:
Arada [10]3 years ago
8 0
Let X be the answers all 48 questions on a multiple-choice test by guessing. 

<span>p = 1/4 </span>

<span>q = 1 - 1/4 = 3/4 </span>

<span>n = 48 </span>

<span>μx = n*p = 48*(1/4) = 12 </span>

<span>σx = sqrt(n*p*q) = sqrt(4/*(1/4)*(3/4)) = 0.8660254038 </span>

<span>P(X = 15) = P(X ≤ 16) - P(X ≤ 14) = P((X - 12)/0.8660254038 ≤ (16 - 12)/0.8660254038) - P((X - 12)/0.8660254038 ≤ (14 - 12)/0.8660254038) = P(Z ≤ 4.62) - P(Z ≤ 2.31) = 1 - 0.9896 = 0.0104 </span>

<span>You could use the binomial distribution: </span>

<span>P(X = 15) = 0.07670882173 </span>

<span>(48) </span>
<span>(15)*((1/4)^15)*(3/4)^33 = 0.07670882173</span>
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