in a given city, 6% of all drivers get at least one parkingticket per year. Use
ID: 2954626 • Letter: I
Question
in a given city, 6% of all drivers get at least one parkingticket per year. Use the poisson approximation to the binomial distribution todetermine the probabilities that among 80 drivers (randomly chosen in this city)? a) 4 will get at least one parking ticket in any givenyear; b) at least 3 will get at least one parking ticket in anygiven year; c) anywhere from 3 to 6, inclusive, will get at least oneparking ticket in any given year; d) at most 10 will get at least one parking ticket in anygiven year; ---------------------------------------------------------- Please explain step by step.. Thank you in advance... in a given city, 6% of all drivers get at least one parkingticket per year. Use the poisson approximation to the binomial distribution todetermine the probabilities that among 80 drivers (randomly chosen in this city)? a) 4 will get at least one parking ticket in any givenyear; b) at least 3 will get at least one parking ticket in anygiven year; c) anywhere from 3 to 6, inclusive, will get at least oneparking ticket in any given year; d) at most 10 will get at least one parking ticket in anygiven year; ---------------------------------------------------------- Please explain step by step.. Thank you in advance...Explanation / Answer
The Poisson approximation of Binomial uses the following assumption:
? = Np = 80(.06) = 4.8
Now use the formula for Poisson in your textbook with ? = 4.8
a) P(X=4) = 0.182
b) P(X>2) = 1 - P(X=0) - P(X=1) - P(X=2) = 0.8575
c) P(3 <=X<=6) = P(X=3)+P(X=4)+P(X=5)+P(X=6) = 0.648
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