It was observed that $150$ vehicles crossed a particular location of a highway in a duration of $30$ minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the number of times headway is greater than $5$ seconds in the above observation ?

98.85

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Solution

The correct option is A 98.85
Probability of time headway greater than t (sec) is given by

$p (h \geq t) = e^{- λ t}$

$λ = \frac{150}{30 \times 60} v e h / s e c$

$p (h \geq 5) = e^{- \frac{150}{30 \times 60} \times 5}$
$= 0.659$

number of times headway is greater than 5 sec
$= 0.659 \times 150 = 98.85$

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It was observed that 150 vehicles crossed a particular location of a highway in a duration of 30 minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the number of times headway is greater than 5 seconds in the above observation ? 98.85

The correct option is A 98.85Probability of time headway greater than t (sec) is given by p(h≥t)=e−λt λ=15030×60 veh/sec p(h≥5)=e−15030×60×5 =0.659 number of times headway is greater than 5 sec =0.659×150=98.85

It was observed that $150$ vehicles crossed a particular location of a highway in a duration of $30$ minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the number of times headway is greater than $5$ seconds in the above observation ?

98.85