At a checkout counter customers arrive at an average of 1.5...

At a checkout counter customers arrive at an average of 1.5 per minute. Find the probabilities that (use the Poisson distribution) (a) At most 4 will arrive in any given minute; (b) At least 3 will arrive during an interval of 2 minutes; (c) At most 15 will arrive during an interval of 6 minutes.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:06 In this question here we're going to discuss about the portion distribution.

00:09 Let me remind you that if we have the x that followed by the possum when the lambda and then the probability of the x equal to k equal to the power minus lambda, lambda power k, divided by k, in this question here, the number of the customer arrived x, it will follow by the possum, and then with the lambda now it will equal to the 1 .5 per minute and now the question i asked you to find the probability that almost 4 will arrive in any given minute so means don't want you find the probability on the x small equal to 4 and then by the formula which you need to turn into the summation k -goat from the zo to the 4 and with the level that equal to 1 .5 we have each of the power minus 1 .5 and 1 .5 power k divided by k photorial.

01:11 Now we can compute this one so let me compute here for you for the poison when the x here equal to the 4 the rate equal to 1 .5 then we get equal to the 0 .9 814 and that will be the answer for the a.

01:39 Now for the b, once you find alice 3 will write 3 an interval of the 2 minutes.

01:45 So this one will be the 2 minutes so therefore i will call the y equal to the number of the customers in 2 minute and therefore why it will follow by the pos sum again but now the rate lambda now equal to 1 minute it will be 1 .5 customer if we have 2 minutes it will will be the 3 per 2 minute here and therefore we will have the probability that the y will be unlisted will be greater equal to 3 and this probability can be easy to consider the complement 1 minus probability of the x of the y smaller equal to the 2 so it equals to 1 minus summation k from 0 to the 2 now the lambda now equal to 3 so each to the bar minus 3, 3 power k, the bannibati, the bannibati factorial.

02:46 And when we compute it, we will have the answer equal to 0 .5768.

03:01 And for the question c, we want to consider the interval of the six minutes...

Question

At a checkout counter customers arrive at an average of 1.5 per minute. Find the probabilities that (use the Poisson distribution) (a) At most 4 will arrive in any given minute; (b) At least 3 will arrive during an interval of 2 minutes; (c) At most 15 will arrive during an interval of 6 minutes.

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