Customers arrive at a checkout counter in a department store...

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of six per hour. Use R to calculate the probabilities of the following occurring during a given hour. (Round your answers to three decimal places.) (a) No more than six customers arrive? (b) At least four customers arrive? (c) Exactly nine customers arrive? Need Help? Read It Submit Answer

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00:01 We're modeling the number of customers per hour at a grocery store, check out.

00:04 We're told the average number is seven customers traveler and were asked to calculate a few probabilities.

00:12 First, the probability that there are no more than three customers in an hour probability that there are at least two and the probability that there are exactly five.

00:23 So for this problem, the concept that will need to views is theis equation for a person distribution and how that allows us to calculate specific probabilities and the idea that ah, the mean for a person distribution is equal to a parameter called lambda.

00:46 And so, for our hassan distribution, we have ah, when a probability oven event x equals lower case x, we can determine that from.

01:00 So this is a specific instance, like x.

01:04 So capital x being the number of customers per hour and small x being, let's say a number three.

01:11 Then that probability can be described by the equation e to the minus lambda times, lambda to the x over x factorial.

01:23 And so we're given our mean here and, um, you so i mean mu is equal to lambda for our plus on distribution, and we're told that that is seven.

01:39 Now we can calculate our specific probabilities.

01:44 So part a.

01:46 Waas.

01:48 We want this x to be less than no more than three.

01:52 So this x is less than or equal to three.

01:56 So probability of x being less than or equal to three.

02:02 It's gonna be equal to soldiers.

02:04 So it's the probability that x is one that x zero or one or two or three so that some of those probabilities the probability of x equals zero plus probability.

02:19 Mexico one.

02:22 It was probably x equal to plus probability.

02:26 X equals three and we can write that so we can write out.

02:33 We'll have four terms for this probability, and we can factor out the e to the minus seven from each of them.

02:42 And so then we'll have four terms inside our effect inside our princess...

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