Question

In: Statistics and Probability

Cars and trucks arrive at a gas station randomly and independently of each other, at an average rate of 17.4 and 9.6 per hour, respectively.

Cars and trucks arrive at a gas station randomly and independently of each other, at an average rate of 17.4 and 9.6 per hour, respectively. Use the Poisson distribution to find the probability that

a. more than 5 cars arrive during the next 16 minutes,

b. we have to wait more than 21 minutes for the arrival of the third truck (from now),

c. the fifth vehicle will take between 17 and 23 minutes (from now) to arrive.

Expert Solution

a) for 16 minutes

λ = 17.4 / hour * 16 min = 17.4 *16/60 = 4.64

P(X> 5) = 1- P(X<= 5) = 1 - 0.67885 = 0.32115

b)

interarrival time is exponential distribution with parameter λ = 9.6/60

P(X <x) = 1 -e^(-λ x)

P(X> x) = e^(-λ x)

P(X > 21) = 1 - F(21) = e^(-21 * 9.6/60) = 0.03473525894

c)

combined λ = 17.4/60 + 9.6/60 = 0.45

P(17 <X< 23)

=P(next vechile arrives<6mins)=

= 1-e^-.45*(6)=0.93279

orchestra answered 2 years ago

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