Mathematics
09.05.2023 04:47
251
293
5
Solved by an expert

Consider a point on the trans-australian highway, where two old wombats live. arrivals

Consider a point on the trans-australian highway, where two old wombats live. arrivals of cars at this point follow a poisson distribution; the average rate of arrivals is 1 car per 12 seconds. 1. one of these old wombats requires 12 seconds to cross the highway, and he starts out immediately after a car goes by. what is the probability he will survive?

(a) 0.114
(b) 0,736
(c) 0.368
(d) 0.184
Show Answers
tinyiaihfurlow
tinyiaihfurlow
4,4(23 marks)

(C) 0.368

Step-by-step explanation:

The Poisson distribution models the probability that an event occurs k times in a given fix interval of time.

Is defined by the probability function

\huge P(k)=\frac{\lambda^ke^{-\lambda}}{k!}

where

k = number of events in the given interval

\huge \lambda = average number of events in the given interval.

In our specific case, the given interval of time is 12 seconds, and \huge \lambda = 1 (1 car  every 12 seconds).

As the old wombat requires 12 seconds to cross the highway, it might survive if only 1 car arrives over those 12 seconds.

The probability of this fact is P(1)

\huge P(1)=\frac{1^1e^{-1}}{1!}=e^{-1}=0.367879\approx 0.368

So, the right answer is (C), 0.368

Cassandoo
Cassandoo
4,4(51 marks)

Just Divide the number by 5 lol

Popular Questions about the subject: Mathematics

Solve the system of equations algebraically. y = 7x + 15 y = 4x + 9...
Mathematics
18.04.2023 02:28
Drag the tiles to the correct boxes to complete the pairs. not all tiles...
Mathematics
07.07.2022 01:12
Write the fraction in simplest form 7/28...
Mathematics
08.08.2022 11:41
If 1+1=6 2+5=7 3+4=9 6+8=8 then, 7+9=...
Mathematics
15.06.2020 00:16
Rectangle efgh is the image of rectangle abcd after a sequence of transformations...
Mathematics
12.12.2022 05:44
What is six times three divided by 2...
Mathematics
01.09.2021 01:43

New questions by subject

Why did chinese build the great walls to the north...
History
16.05.2022 14:43
Aserver to cook ratio of 5 to 2. the total number of cooks and servers are...
Mathematics
14.05.2020 19:06
#
#
#
#
# #

We expand our knowledge with many expert answers