In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years older has been involved in Complete parts (a) through (1) below Which of the following interpretations of the mean is correct? OA. If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be equal to the mean number of marriages for most individuals OB. If any number of individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable OC. If many randomly selected individuals 40 to 49 years of age were surveyed, the sample mean number of marriages should be close to the mean of the random variable OD. If many individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable. OE. If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be less than the mean number of marriages for most individuals (d) Compute the standard deviation of the random variable X ox-marriages (Round to one decimal place as needed) (e) What is the probability that a randomly selected individual 15 years or older was involved in two marriages? P(x) -> 0274 1 0579 0.119 0.023 0.004 0001 8105445
In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years older has been involved in Complete parts (a) through (1) below Which of the following interpretations of the mean is correct? OA. If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be equal to the mean number of marriages for most individuals OB. If any number of individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable OC. If many randomly selected individuals 40 to 49 years of age were surveyed, the sample mean number of marriages should be close to the mean of the random variable OD. If many individuals aged 15 year or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable. OE. If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be less than the mean number of marriages for most individuals (d) Compute the standard deviation of the random variable X ox-marriages (Round to one decimal place as needed) (e) What is the probability that a randomly selected individual 15 years or older was involved in two marriages? P(x) -> 0274 1 0579 0.119 0.023 0.004 0001 8105445
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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![**Understanding the Mean and Standard Deviation of Marriages for Individuals Aged 15 Years and Older**
In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below.
### Distribution Table:
| x | P(X) |
|----|--------|
| 0 | 0.274 |
| 1 | 0.579 |
| 2 | 0.119 |
| 3 | 0.023 |
| 4 | 0.004 |
| 5 | 0.001 |
### Analysis:
#### (a) Interpretation of the Mean:
Which of the following interpretations of the mean is correct?
- **A.** If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be equal to the mean number of marriages for most individuals.
- **B.** If any number of individuals aged 15 years or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
- **C.** If many randomly selected individuals 40 to 49 years of age were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
- **D.** If many individuals aged 15 years or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
- **E.** If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be less than the mean number of marriages for most individuals.
#### (b) Calculating the Mean:
To calculate the mean number of marriages (μ), the formula used is:
\[ \mu = \sum [x \cdot P(X)] \]
#### (d) Compute the Standard Deviation of X:
Compute the standard deviation of the random variable X.
\[ \sigma_X = \sqrt{\sum [x^2 \cdot P(X)] - \mu^2} \]
(Round to one decimal place as needed.)
#### (e) Probability of Exactly Two Marriages:
What is the probability that a randomly selected individual aged 15 years or older was involved in two marriages?
(Type an integer or a decimal. Do not round.)
\[ P(X = 2) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd86b4514-aa18-4e84-8d65-86fc6c642f07%2F384a74c4-7add-410a-9ba9-742a9d13a0c5%2Fbz63xvm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Mean and Standard Deviation of Marriages for Individuals Aged 15 Years and Older**
In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Complete parts (a) through (f) below.
### Distribution Table:
| x | P(X) |
|----|--------|
| 0 | 0.274 |
| 1 | 0.579 |
| 2 | 0.119 |
| 3 | 0.023 |
| 4 | 0.004 |
| 5 | 0.001 |
### Analysis:
#### (a) Interpretation of the Mean:
Which of the following interpretations of the mean is correct?
- **A.** If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be equal to the mean number of marriages for most individuals.
- **B.** If any number of individuals aged 15 years or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
- **C.** If many randomly selected individuals 40 to 49 years of age were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
- **D.** If many individuals aged 15 years or older were surveyed, the sample mean number of marriages should be close to the mean of the random variable.
- **E.** If many randomly selected individuals aged 15 years or older were surveyed, the observed number of marriages will be less than the mean number of marriages for most individuals.
#### (b) Calculating the Mean:
To calculate the mean number of marriages (μ), the formula used is:
\[ \mu = \sum [x \cdot P(X)] \]
#### (d) Compute the Standard Deviation of X:
Compute the standard deviation of the random variable X.
\[ \sigma_X = \sqrt{\sum [x^2 \cdot P(X)] - \mu^2} \]
(Round to one decimal place as needed.)
#### (e) Probability of Exactly Two Marriages:
What is the probability that a randomly selected individual aged 15 years or older was involved in two marriages?
(Type an integer or a decimal. Do not round.)
\[ P(X = 2) =
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