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quiz_04_31mar2010_solution

# quiz_04_31mar2010_solution - of an 80 chance that an...

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Statistics 100 Quiz 4 Wednesday 31 March 2010 Name: Section TF/day and time: Suppose that Harvard admits 2050 students for each September’s freshman class and that there is an 80% chance that an admitted student will decide to accept the oﬀer to attend Harvard. 1. What is the mean and standard deviation of the number of students who decide to attend? Solution: Let X be the number of students who accept oﬀers, then X Bin(2050 , 0 . 8). E ( X ) = np = 2050(0 . 8) = 1640 σ X = p np (1 - p ) = p 2050(0 . 8)(0 . 2) = 18 . 11 2. Suppose Harvard has dormitory room spots for only 1655 freshman. Under the assumption
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Unformatted text preview: of an 80% chance that an admitted student will attend Harvard, what is the probability that Harvard will not have enough dormitory room spots for the freshman students? Solution: We will use normal approximation to solve this question. First let’s verify the conditions: np = 1640 > 10 and n (1-p ) = 2050(0 . 2) = 410 > 10 So X is approximately N ( μ X ,σ X ) = N (1640 , 18 . 11). P ( X > 1655) = P ( Z > 1655-1640 18 . 11 ) = P ( Z > . 828) = 0 . 204 . Page 1 of 1...
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