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A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c. X 0 P(X=x) 0.0857 1 0.2447 2 0.3208 3 0.2415 4 0 0.1073 *** i ne mean number of children in a family with four girls iS b. Obtain the standard deviation of the random variable. 0= 1.1209 (Round to four decimal places as needed.) c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below. 4 B. O C. D. Number of Girls Number of Girls Number of Girls Number of Girls 0.5- 0.5 0.5 0.5 0.4- 0.3- 0.4- 0.4 0.3- 0.2- 0.2- 0.2- 0.1- 0.1- 0.1- 0- 0- 0012 01234 0 1 2 3 4 01234 01234 The mean is 2.0400. (Type an integer or decimal rounded to four decimal places as needed.) The one-standard-deviation interval is.. the two-standard-deviation interval is.. and the three-standard-deviation interval is 0 (Type integers or decimals rounded to four decimal places as needed. Use ascending order.) Clear all Check answer Help me solve this View an example Get more help. A S MacBook Air Probability 0.4- 0.3- Probability 24 0.3 0.2 0.1- 0-

A census collected data on everyone that lived in a certain small town. The random variable X is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c. X 0 P(X=x) 0.0857 1 0.2447 2 0.3208 3 0.2415 4 0 0.1073 *** i ne mean number of children in a family with four girls iS b. Obtain the standard deviation of the random variable. 0= 1.1209 (Round to four decimal places as needed.) c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals. Choose the correct histogram below. 4 B. O C. D. Number of Girls Number of Girls Number of Girls Number of Girls 0.5- 0.5 0.5 0.5 0.4- 0.3- 0.4- 0.4 0.3- 0.2- 0.2- 0.2- 0.1- 0.1- 0.1- 0- 0- 0012 01234 0 1 2 3 4 01234 01234 The mean is 2.0400. (Type an integer or decimal rounded to four decimal places as needed.) The one-standard-deviation interval is.. the two-standard-deviation interval is.. and the three-standard-deviation interval is 0 (Type integers or decimals rounded to four decimal places as needed. Use ascending order.) Clear all Check answer Help me solve this View an example Get more help. A S MacBook Air Probability 0.4- 0.3- Probability 24 0.3 0.2 0.1- 0-

MATLAB: An Introduction with Applications
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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### Probability Distribution Analysis for Number of Girls in a Family A census collected data on everyone that lived in a certain small town. The random variable \( X \) is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below: | \( x \) | 0 | 1 | 2 | 3 | 4 | |-------------|------|------|------|------|------| | \( P(X=x) \) | 0.0857 | 0.2447 | 0.3208 | 0.2415 | 0.1073 | #### Tasks: 1. **Calculate the Mean Number of Children in a Family with Four Girls** - The mean number of children in a family with four children is calculated as the expected value of \( X \). 2. **Obtain the Standard Deviation of the Random Variable** - The standard deviation of the random variable \( X \) is \( \sigma = 1.1209 \) (rounded to four decimal places as needed). 3. **Construct a Probability Histogram and Locate Standard-Deviation Intervals** - A correct probability histogram for the random variable should be constructed. The histogram should show the mean, and one-, two-, and three-standard-deviation intervals. #### Probability Histograms **Correct Histogram Identification**: - Four options labeled A, B, C, and D depict the probability histograms for the number of girls in a family. **Graph B** appears to be the correct histogram: - The graph displays the probabilities of having 0, 1, 2, 3, or 4 girls in a family. - The probabilities are visually represented by the heights of bars corresponding to each \( x \) value (i.e., 0, 1, 2, 3, and 4). **Describing the Histograms**: - **Option A**: Incorrect histogram. - **Option B**: Correct histogram. The distribution fits the given probabilities. - **Option C**: Incorrect histogram. - **Option D**: Incorrect histogram. #### Calculations - The mean (\( \mu \)) is calculated as 2.0400 (rounded to four decimal places as needed). - To determine the one-standard-deviation interval, two-standard-deviation interval, and three-standard-deviation interval around the mean:
Transcribed Image Text:### Probability Distribution Analysis for Number of Girls in a Family A census collected data on everyone that lived in a certain small town. The random variable \( X \) is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below: | \( x \) | 0 | 1 | 2 | 3 | 4 | |-------------|------|------|------|------|------| | \( P(X=x) \) | 0.0857 | 0.2447 | 0.3208 | 0.2415 | 0.1073 | #### Tasks: 1. **Calculate the Mean Number of Children in a Family with Four Girls** - The mean number of children in a family with four children is calculated as the expected value of \( X \). 2. **Obtain the Standard Deviation of the Random Variable** - The standard deviation of the random variable \( X \) is \( \sigma = 1.1209 \) (rounded to four decimal places as needed). 3. **Construct a Probability Histogram and Locate Standard-Deviation Intervals** - A correct probability histogram for the random variable should be constructed. The histogram should show the mean, and one-, two-, and three-standard-deviation intervals. #### Probability Histograms **Correct Histogram Identification**: - Four options labeled A, B, C, and D depict the probability histograms for the number of girls in a family. **Graph B** appears to be the correct histogram: - The graph displays the probabilities of having 0, 1, 2, 3, or 4 girls in a family. - The probabilities are visually represented by the heights of bars corresponding to each \( x \) value (i.e., 0, 1, 2, 3, and 4). **Describing the Histograms**: - **Option A**: Incorrect histogram. - **Option B**: Correct histogram. The distribution fits the given probabilities. - **Option C**: Incorrect histogram. - **Option D**: Incorrect histogram. #### Calculations - The mean (\( \mu \)) is calculated as 2.0400 (rounded to four decimal places as needed). - To determine the one-standard-deviation interval, two-standard-deviation interval, and three-standard-deviation interval around the mean:
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