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klio [65]
3 years ago
14

On a multiple choice test with 15 ​questions, each question has four possible​ answers, one of which is correct. For students wh

o guess at all​ answers, find the variance for the number of correct answers. Round to the nearest tenth.
Mathematics
1 answer:
Aleks [24]3 years ago
5 0

Answer:

The variance for the number of correct answers is 2.8 questions

Step-by-step explanation:

The number of correct answers follows binomial distribution, in which we have:

  • n identical and independents events: the 15 questions
  • two possibles results that we call success and fail: The answer is correct and the answer is incorrect
  • probability p of success and 1-p of fail. Probability 1/4 of get the answer correct and probability of 3/4 of get the answer incorrect. This probabilities are calculated on that way because every question have 4 possible answers and one of which is correct.

So, the variance for a variable x that follows a Binomial distributions is:

V(x)=n*p*(1-p)

Then, the variance for the number of correct answers is:

V(x)=15*(1/4)*(3/4) = 2.8125 ≈ 2.8

Because n is equal to 15, p is equal to 1/4 and (1-p) is equal to 3/4.

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