6. For the six customers simulated above, what is the average waiting time? 7. If the random number generated for the inter arrival time for the 7th customer is 88, then when will the 7th customer arrive?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Operations and production management questions.
![6. For the six customers simulated above, what is the average waiting time?
7. If the random number generated for the inter arrival time for the 7th customer is 88, then
when will the 7th customer arrive?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25639db5-7a82-42fc-9741-06d4b74ed5e9%2Fdfc6b78d-b898-4cab-a762-3d051feb8c83%2F04gu24_processed.png&w=3840&q=75)
![The manager of a small post office is concerned that the growing township is overloading the
one-window service being offered. Sample data are collected on 100 individuals who arrive for
service:
Inter arrival time
(Time between
Arrivals)
(minutes)
Frequency
1
8.
2
35
3
40
4
17
Service Time
(minutes)
Frequency
1
12
21
3
41
4
26
Using the following random number sequence, simulate six arrivals, assume the first arrival is
time 0.
RN for arrivals: 08, 74, 24, 34, 45, 86
RN for service time: 31, 32, 45, 53, 78, 67
(Note: we don't need to use the random number 08 for first arrival, since we assume the first
arrival is time 0)
1. At what time will the second customer arrive?
2. What is the time required to serve the third customer?
3. When does the operator begin processing the fourth customer?
4. How long does the fifth customer wait in line?
5. When the sixth customer arrives, will the customer get served right away? Simply answer
Yes or No.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25639db5-7a82-42fc-9741-06d4b74ed5e9%2Fdfc6b78d-b898-4cab-a762-3d051feb8c83%2F5qhjmcb_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)