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Unformatted text preview: Solutions to Midterm 2 Problem 1. 1. A traffic control engineer reports that 75 % of the vehicles passing through a check point are from within the state. What is the probability that at least three of the next five vehicles are from out of state? 2. A homeowner plants six bulbs selected at random from a box containing five tulip bulbs and four daffodil bulbs. What is the probability that he planted two daffodil bulbs and four tulip bulbs? Solution. 1. This is a binomial problem. The probability of success (out of state) is p = . 25 and n = 5. We are looking at P ( X ≥ 3) where X ∼ Bin (5 , 1 / 4), which is P ( X = 3) + P ( X = 4) + P ( X = 5) = 53 / 512 = 0 . 103516 . 2. This is a hypergeometic distribution problem with the parameters N = 9, M = 5 (the number of tulips), n = 6, and thus the probability we are looking for is P ( X = 4) = ( 5 4 )( 4 2 ) ( 9 6 ) = 5 14 = 0 . 357 . Problem 2. 1. The amount of coke in the 2-liter bottles has a normal distribution with mean 2.05 liter and standard deviation of .1. If you bought a 2-liter bottle of coke, whatmean 2....
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This note was uploaded on 05/26/2010 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.
- Spring '08