Revision as of 23:36, 26 June 2024 by Admin (Created page with "A true-false examination has 48 questions. June has probability 3/4 of answering a question correctly. April just guesses on each question. A passing score is 30 or more correct answers. Compare the probability that June passes the exam with the probability that April passes it. '''References''' {{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date...")
ABy Admin
Jun 27'24
Exercise
A true-false examination has 48 questions. June has probability 3/4 of answering a question correctly. April just guesses on each question. A passing score is 30 or more correct answers. Compare the probability that June passes the exam with the probability that April passes it.
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.
ABy Admin
Jun 27'24
Solution: E
By the central limit theorem, June's score is approximately normally distributed with mean 48*3/4 = 36 and variance 48 * 3/4 * 1/4 = 9. Therefore the probability that June passes the exam is approximately equal to the probability that a standard normal variable exceeds (30-36)/3 = -2. This is approximately equal to 0.9773.