The accompanying data represent the ideal number of children for a random sample of 900 adults. Complete parts (a) through (d) below. E Click the icon to view the data about ideal numbers of children. (a) Construct a discrete probability distribution for the random variable x. x (# of children) P(x) 3 4. 6 (Round to three decimal places as needed.) (b) Draw a graph of the probability distribution. Choose the correct graph below. OA. OB. Oc. OD. Ideal Number of Children Ideal Number of Children Ideal Number of Children Ideal Number of Children 0.6- 0.5- 0.4- 0.3- 0.6 0.5- 03 Q 0.6 0.5- 04- 0.3- 02- i 0.1- 0.6- 0.5- 0.4- 03- 0.2- a 0.1- 0.1- a 0.1- 우우 01234 56 Number of Children 0123456 Number of Children ói2 3 4 5 6 Number of Children 012345 6 Number of Children (c) Compute and interpret the mean of the random variable X. The mean is children. (Round to one decimal place as needed.) Which of the following interpretations of the mean is correct? O Time Remaining: 02:40:47
The accompanying data represent the ideal number of children for a random sample of 900 adults. Complete parts (a) through (d) below. E Click the icon to view the data about ideal numbers of children. (a) Construct a discrete probability distribution for the random variable x. x (# of children) P(x) 3 4. 6 (Round to three decimal places as needed.) (b) Draw a graph of the probability distribution. Choose the correct graph below. OA. OB. Oc. OD. Ideal Number of Children Ideal Number of Children Ideal Number of Children Ideal Number of Children 0.6- 0.5- 0.4- 0.3- 0.6 0.5- 03 Q 0.6 0.5- 04- 0.3- 02- i 0.1- 0.6- 0.5- 0.4- 03- 0.2- a 0.1- 0.1- a 0.1- 우우 01234 56 Number of Children 0123456 Number of Children ói2 3 4 5 6 Number of Children 012345 6 Number of Children (c) Compute and interpret the mean of the random variable X. The mean is children. (Round to one decimal place as needed.) Which of the following interpretations of the mean is correct? O Time Remaining: 02:40:47
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
Transcribed Image Text:### Probability Distribution of the Ideal Number of Children
#### Graph Explanation
The graph titled "Ideal Number of Children" displays a probability distribution for the number of children. The horizontal axis is labeled "Number of Children," ranging from 0 to 6. The vertical axis represents the probability, labeled from 0 to 0.5. Red vertical lines indicate the probability of each number of children.
#### Data Table
The table titled "Ideal number of children data" includes two columns:
- **x (# of children):** Represents the number of children, ranging from 0 to 6.
- **Frequency:** Indicates how many people, in the survey, considered each number of children as ideal.
| x (# of children) | Frequency |
|-------------------|-----------|
| 0 | 11 |
| 1 | 31 |
| 2 | 514 |
| 3 | 259 |
| 4 | 67 |
| 5 | 16 |
| 6 | 2 |
### Analysis Process
- To interpret the mean of the random variable \( X \) (ideal number of children):
- Calculate the expected value based on the frequency data.
- Interpretations involve considering survey results, projecting the mean ideal number of children, and comparing observed data to typical expectations.
### Calculations
- The mean and standard deviation of the random variable \( X \) need to be calculated using the data provided, with guidance to round to the nearest decimal place when necessary.
- **Mean Interpretation:**
- When the sample size increases, the mean ideal number of children converges to the population's general perception, highlighted by the most frequent response in the dataset.
Other instructions ask for identifying correct interpretations of the mean, emphasizing the expected values based on survey sizes, and understanding distribution characteristics.
Transcribed Image Text:The image displays a problem regarding the ideal number of children based on a random sample of 900 adults. The task involves multiple steps:
(a) **Construct a discrete probability distribution for the random variable X.**
- A table is partially presented with columns for the number of children (X) ranging from 0 to 6 and a column for the probability (P(x)), which is blank. Instructions are provided to round the probability to three decimal places as needed.
(b) **Draw a graph of the probability distribution. Choose the correct graph below.**
Four graph options labeled A, B, C, and D are available. Each graph plots "Probability" on the vertical axis against "Ideal Number of Children" on the horizontal axis, with potential ideal numbers of children ranging from 0 to 6.
(c) **Compute and interpret the mean of the random variable X.**
- A field is provided to enter the mean number of children, with an instruction to round to one decimal place.
- The text asks, "Which of the following interpretations of the mean is correct?"
(d) Part (d) is not visible in the image.
The accompanying graphs are similar bar charts with varying heights representing the probability for each ideal number of children from 0 to 6.
Additional elements:
- The page contains a timer at the bottom right, showing "Time Remaining: 02:40:47".
Expert Solution
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 2 steps with 1 images
