The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c X 4 5 6 2 P(X=x) 0.025 0.045 0.306 7 8 0 0.187 0.431 0.006 a. Find and interpret the mean of the random variable. = 5.947 (Round to three decimal places as needed.) Interpret the mean. Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) OA. The average number of persons in a shuttle crew is person(s). OB. The most common number of persons in a shuttle crew is person(s).
The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c X 4 5 6 2 P(X=x) 0.025 0.045 0.306 7 8 0 0.187 0.431 0.006 a. Find and interpret the mean of the random variable. = 5.947 (Round to three decimal places as needed.) Interpret the mean. Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) OA. The average number of persons in a shuttle crew is person(s). OB. The most common number of persons in a shuttle crew is person(s).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![The random variable \(X\) is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.
| x | 2 | 4 | 5 | 6 | 7 | 8 |
|-------|-------|-------|-------|-------|-------|-------|
| P(X=x)| 0.025 | 0.045 | 0.306 | 0.187 | 0.431 | 0.006 |
**a. Find and interpret the mean of the random variable.**
\[
\mu = 5.947 \quad \text{(Round to three decimal places as needed.)}
\]
**Interpret the mean. Select the correct choice below and fill in the answer box to complete your choice.**
(Round to three decimal places as needed.)
- [ ] A. The average number of persons in a shuttle crew is \(\boxed{5.947}\) person(s).
- [ ] B. The most common number of persons in a shuttle crew is \(\boxed{5.947}\) person(s).
**Explanation:**
The column labeled \( x \) represents the possible crew sizes, while the column labeled \( P(X=x) \) represents their respective probabilities. To calculate the mean \(\mu\) of the random variable X, we sum the products of each value of \( x \) and its corresponding probability (\( P(X=x) \)):
\[
\mu = \sum (x \times P(X=x)) = (2 \times 0.025) + (4 \times 0.045) + (5 \times 0.306) + (6 \times 0.187) + (7 \times 0.431) + (8 \times 0.006)
\]
\[
\mu = 0.05 + 0.18 + 1.53 + 1.122 + 3.017 + 0.048 = 5.947
\]
To interpret the mean:
- **Option A** (correct): The mean represents the average number of persons in the shuttle crew, 5.947.
- **Option B**: This option refers to the mode, which is the most frequently occurring value. It does not represent the mean.
Note: There are no graphs or diagrams to explain in this image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02ebb731-29eb-4cd6-ba2a-cc2ff28bf3c8%2F09bdb69f-f03f-4c69-9306-243bcf0e2931%2F5wpbxyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The random variable \(X\) is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.
| x | 2 | 4 | 5 | 6 | 7 | 8 |
|-------|-------|-------|-------|-------|-------|-------|
| P(X=x)| 0.025 | 0.045 | 0.306 | 0.187 | 0.431 | 0.006 |
**a. Find and interpret the mean of the random variable.**
\[
\mu = 5.947 \quad \text{(Round to three decimal places as needed.)}
\]
**Interpret the mean. Select the correct choice below and fill in the answer box to complete your choice.**
(Round to three decimal places as needed.)
- [ ] A. The average number of persons in a shuttle crew is \(\boxed{5.947}\) person(s).
- [ ] B. The most common number of persons in a shuttle crew is \(\boxed{5.947}\) person(s).
**Explanation:**
The column labeled \( x \) represents the possible crew sizes, while the column labeled \( P(X=x) \) represents their respective probabilities. To calculate the mean \(\mu\) of the random variable X, we sum the products of each value of \( x \) and its corresponding probability (\( P(X=x) \)):
\[
\mu = \sum (x \times P(X=x)) = (2 \times 0.025) + (4 \times 0.045) + (5 \times 0.306) + (6 \times 0.187) + (7 \times 0.431) + (8 \times 0.006)
\]
\[
\mu = 0.05 + 0.18 + 1.53 + 1.122 + 3.017 + 0.048 = 5.947
\]
To interpret the mean:
- **Option A** (correct): The mean represents the average number of persons in the shuttle crew, 5.947.
- **Option B**: This option refers to the mode, which is the most frequently occurring value. It does not represent the mean.
Note: There are no graphs or diagrams to explain in this image.
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