Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. 3 4 5 P(x) 0.10 0.20 0.35 0.20 0.10 0.05 x Part 1 of 3 Send data to Excel Hy Part: 1/3 0 (a) Compute the mean μx. Round the answer to two decimal places. Part 2 of 3 Next Part 1 2.15 ox= 2 (b) Compute the standard deviation ox. Round your answer to 4 decimal places if necessary. X X S S MacBook Air Español 4 Olh Submit Assignment © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 2
Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. 3 4 5 P(x) 0.10 0.20 0.35 0.20 0.10 0.05 x Part 1 of 3 Send data to Excel Hy Part: 1/3 0 (a) Compute the mean μx. Round the answer to two decimal places. Part 2 of 3 Next Part 1 2.15 ox= 2 (b) Compute the standard deviation ox. Round your answer to 4 decimal places if necessary. X X S S MacBook Air Español 4 Olh Submit Assignment © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Probability Distribution Analysis of Customers in Line at a Supermarket Express Checkout Counter
**Context**: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution:
| \( x \) | 0 | 1 | 2 | 3 | 4 | 5 |
|:---------:|:----:|:---:|:---:|:---:|:---:|:---:|
| \( P(x) \) | 0.10 | 0.20 | 0.35 | 0.20 | 0.10 | 0.05 |
### Step-by-Step Calculation
#### Part 1 of 3
**(a) Compute the mean \(\mu_X\)**. Round the answer to two decimal places.
The mean \(\mu_X\) or expected value \(E(X)\) is calculated using the formula:
\[ \mu_X = \sum (x \cdot P(x)) \]
**Calculation:**
\[ \mu_X = 0 \cdot 0.10 + 1 \cdot 0.20 + 2 \cdot 0.35 + 3 \cdot 0.20 + 4 \cdot 0.10 + 5 \cdot 0.05 \]
\[ \mu_X = 0 + 0.20 + 0.70 + 0.60 + 0.40 + 0.25 \]
\[ \mu_X = 2.15 \]
Therefore, the mean \(\mu_X\) is **2.15**.
#### Part 2 of 3
**(b) Compute the standard deviation \(\sigma_X\)**. Round your answer to four decimal places if necessary.
The standard deviation \(\sigma_X\) is calculated using the formula:
\[ \sigma_X = \sqrt{\sum ((x - \mu_X)^2 \cdot P(x))} \]
**Calculation:**
\[ \sigma_X = \sqrt{(0 - 2.15)^2 \cdot 0.10 + (1 - 2.15)^2 \cdot 0.20 + (2 - 2.15)^2 \cdot 0.35 + (3 - 2.15)^2 \cdot 0.20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29a07bd8-eb1c-498d-b0a8-9eb9d6fddf09%2F7151918d-27ab-4f26-a0b4-19ebe3497d16%2Fo2qgqh4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Distribution Analysis of Customers in Line at a Supermarket Express Checkout Counter
**Context**: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution:
| \( x \) | 0 | 1 | 2 | 3 | 4 | 5 |
|:---------:|:----:|:---:|:---:|:---:|:---:|:---:|
| \( P(x) \) | 0.10 | 0.20 | 0.35 | 0.20 | 0.10 | 0.05 |
### Step-by-Step Calculation
#### Part 1 of 3
**(a) Compute the mean \(\mu_X\)**. Round the answer to two decimal places.
The mean \(\mu_X\) or expected value \(E(X)\) is calculated using the formula:
\[ \mu_X = \sum (x \cdot P(x)) \]
**Calculation:**
\[ \mu_X = 0 \cdot 0.10 + 1 \cdot 0.20 + 2 \cdot 0.35 + 3 \cdot 0.20 + 4 \cdot 0.10 + 5 \cdot 0.05 \]
\[ \mu_X = 0 + 0.20 + 0.70 + 0.60 + 0.40 + 0.25 \]
\[ \mu_X = 2.15 \]
Therefore, the mean \(\mu_X\) is **2.15**.
#### Part 2 of 3
**(b) Compute the standard deviation \(\sigma_X\)**. Round your answer to four decimal places if necessary.
The standard deviation \(\sigma_X\) is calculated using the formula:
\[ \sigma_X = \sqrt{\sum ((x - \mu_X)^2 \cdot P(x))} \]
**Calculation:**
\[ \sigma_X = \sqrt{(0 - 2.15)^2 \cdot 0.10 + (1 - 2.15)^2 \cdot 0.20 + (2 - 2.15)^2 \cdot 0.35 + (3 - 2.15)^2 \cdot 0.20
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman