180asolns4 - 180 HW 4 Solutions 1) Jimmy rides his old...

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180 HW 4 Solutions 1) Jimmy rides his old motorcycle every day of the year. The motorcycle starts with probability 1 / 2 each time Jimmy presses on the starter. Compute the probability that in a given year (365 days) Jimmy has to press the starter at least 3 times to start the motorcycle on more than 300 days. Answer Note that the number of presses it takes to start the motorcycle on any given day follows a geometric distribution with probability 1 / 2 . The probability that it takes at least 3 presses to start the motorcycle on a given day is, thus, 1 - 1 / 2 + (1 / 2) 2 = 1 / 4 . Let X denote the number of days that it takes at least 3 presses to start. Then X Bin (365 , 1 / 4) . Thus P ( X > 300) = P ( X 301) = 365 X i =301 ± 365 i ¶± 1 4 i ± 3 4 365 - i Using the normal approximation, with μ = np = 90 . 25 and σ = p np (1 - p ) = 8 . 27 , we further get P ( X 301) = P (301 X 365) Φ ± 365 - 1 / 2 - 90 . 25 8 . 27 - Φ ± 301 - 1 / 2 - 90 . 25 8 . 27 0
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This homework help was uploaded on 02/03/2008 for the course MATH MATH 180A taught by Professor Castro during the Fall '08 term at UCSD.

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180asolns4 - 180 HW 4 Solutions 1) Jimmy rides his old...

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