A study of the checkout lines at the Safeway Supermarket in...

Name: Problem 49, Chapter 6: Basic Statistics for Business & Economics
Uploaded: 2022-01-23T21:10:02-08:00
Duration: 3 min 56 s
Channel: Jon Southam
Description: A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 p.m. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find: a. No customers are waiting? b. Four customers are waiting? c. Four or fewer are waiting? d. Four or more are waiting?

A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 p.m. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find: a. No customers are waiting? b. Four customers are waiting? c. Four or fewer are waiting? d. Four or more are waiting?

A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 p.m. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find:
a. No customers are waiting?
b. Four customers are waiting?
c. Four or fewer are waiting?
d. Four or more are waiting?

Key Concepts

Poisson Distribution

The Poisson distribution is a discrete probability distribution used to model the number of events occurring within a fixed interval of time or space. It is particularly suitable for situations where events happen independently and at a constant average rate, which is the case in scenarios like the number of customers arriving at a checkout line.

Mean (Lambda, ?)

The parameter ? in the Poisson distribution represents the expected number of events (or customers, in this context) within the given interval. It is a crucial value because it defines the distribution entirely and is used in calculating probabilities using the Poisson formula.

Probability Mass Function (PMF)

The Poisson probability mass function (PMF) provides the probability of observing exactly k events in the fixed interval. The formula is P(X = k) = (?^k * e^(-?)) / k!, where k is a non-negative integer. This function is used to compute the probability for a specific number of occurrences.

Cumulative Distribution Function (CDF)

The cumulative distribution function (CDF) for the Poisson distribution gives the probability of observing at most a certain number of events, i.e., P(X ? k). It is obtained by summing the probabilities from 0 to k as provided by the PMF, and is useful when calculating the probability of a range of outcomes.

Transcript

00:01 All right, so we're looking at safeway, and we're looking at how many people are in line between the hours of 4 and 7 p .m.

00:11 On weekdays.

00:13 There's an average of 4, and what's the probability that if we visit safeway during this time period, we'll find no customers, four customers, four fewer, or four more? so for this, we're going to use the poisson probability distribution, because it's very safe.

00:34 Similar to a binomial in sense that you could be there or not be there.

00:41 But because we're dealing with a time interval and we're dealing with like discrete numbers, but we can have a large number of them.

00:53 We're going to use a poisson distribution.

00:58 So we're given the mean is four.

01:03 So we're told that mu is four.

01:06 So we're going to use that here in a moment.

01:07 Moment for and then we're going to use our poisson probability distribution given here so equals mu which is four to the x i've got zero here that's the x times e xp parentheses negative four time no divided by excuse me x factorial and there we're going to copy and paste it down to five just to for the sake of a bit there.

01:50 And this gives us the possibilities for exactly one, exactly two, three, four, or five, et cetera.

01:56 And we want no customers.

01:57 Well, that's this value here.

01:59 So 0 .018.

02:05 That exactly four are waiting in line.

02:07 Well, that equals this value.

02:09 So 0 .195.

02:12 Right here.

02:13 That's what i'm reading it right here.

02:15 That's a probability for four.

02:16 Four, or whipsies, my formatting here should not be.

02:20 Let me clear this out.