On average 6.5 traffic accidents occur on a particular stretch of road during a

Question

On average 6.5 traffic accidents occur on a particular stretch of road during a week. Assume number of accidents follow a Poisson distribution.

a) What is the mean time between accidents?

b) What is the probability that there will be an accident within the next 12 hours?

c) What is the probability that it will be more than two days before the next accident occurs?

Please show all of your work. I am using this as a study aid. if you are writing this out by hand please make sure your work is legible. thank you

Explanation / Answer

a)

There are 6.5 accidents per week (7*24 = 168 hrs).

Hence, the mean time between accidents is 168/6.5 = 25.84615385 hours. [ANSWER]

********************

b)

For exponentially distributed variables,

P(x<c) = 1 - exp(-c/u)

As u = 25.84615385, then

P(x<12) = 1 - exp(-12/25.84615385) = 0.371416067 [ANSWER]

*********************

c)
Note that 2 days = 48 hours.

For exponentially distributed variables,

P(x>c) = exp(-c/u)

As u = 25.84615385, then

P(x>48) = exp(-48/25.84615385) = 0.156118045 [ANSWER]

**************************

Hi! If you are using a different distrbution for inter-arrival times, please resubmit this question together with the distirbution you use. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.