00:01
So our question says that the number of accidents that occurs at a busy intersection is poisoned distributed with a mean of 3 .5 per week.
00:07
So we are supposed to find the probability of the following event.
00:10
We have question a down to question c.
00:14
So since our distribution follows a poison distribution, we are going to be saying that when a random variable x follows a poison distribution, it's dependent on lambda.
00:24
Where lambda is actually the fixed rate or we can say the mean rates at which the event is occurring.
00:29
So for this question of r's, our lambda is actually equals to 3 .5 per week.
00:38
So the probability mass function that defines a poison distribution is given us probability into bracket x is equal to x is a cost to x is a cost to e raised by minus lambda.
00:48
That lambda raised the power of x divided by x factorial.
00:52
So for the first question, it says, probability that no accidents occurs in one week.
00:56
So probability that x is equals to zero.
00:59
So that's question one.
01:00
And that's going to be erasper minus 3 .5 times 3 .5 raised the power of 0 divided by 0 factorial and that's going to be erasper minus 3 .5 times 1 divided by 1.
01:14
Using our calculator to do the math, we have a irisper minus 3 .5 and that gives us 0 .0302.
01:24
So the probability that no accident occurs in one week is going to be 0 .0302.
01:30
The second question says what is probability that 10 or more accidents occur in a week? so probability that x is greater than or equals to 10.
01:38
This can be written as 1 minus probability that x is lesser than or equals to 9.
01:44
Then we can use a cumulative binomial distribution table, excuse me, a cumulative poison distribution table rather to get this value...