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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 59E
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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
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