Question 1121493: Estimate the indicated probability by using the normal distribution as an approximation of the binomial distribution. A multiple choice exam consists of 60 questions. Each question has 4 possible answers of which one is correct. If all the answers are random guesses, calculate the probability of obtaining at least 20% of correct answers.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 20% = 20/100 = 1/5
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1/5 * 60 = 12 questions
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Probability (P) ( guessing at least 12 questions correctly out of 60 ) = 1 - P (guessing less than 12 questions correctly)
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using normal distribution, we calculate P (X < 12) including the correction factor of -0.5
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P of guessing one answer correctly is 1/4 and 60 * 1/4 = 15(this is our mean)
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standard deviation = sqrt(1/4 * 3/4 * 60) = 3.3541
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apply 0.5 correction factor to 12, 12 - 0.5 = 11.5
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Z(11.5) = (11.5 - 15) / 3.3541 = -1.0435 approximately -1.04
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next we look for the associate probability in the table of z-values, it is 0.1492
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1 - 0.1492 = 0.8508 approximately 0.85
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Probability (P) ( guessing at least 12 questions correctly out of 60 ) = 0.85
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Note the binomial probability for guessing at least 12 questions correctly out of 60 is 0.852
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