**Exercise 19: Probability Distribution of Student Ages at Freshman Orientation**The table below represents the ages of students attending a freshman college orientation course:| Age | # of Students ||-----|---------------|| 20 | 6 || 21 | 7 || 22 | 16 || 23 | 8 || 24 | 4 || 25 | 9 |**a. Construct a Probability Distribution**To construct the probability distribution, calculate the probability for each age by dividing the number of students of that age by the total number of students. - Total number of students = 50**b. Graph the Probability Distribution Using a Histogram**Create a histogram with the age on the x-axis and the probability on the y-axis. Each bar represents the probability of a student being a certain age.**c. Calculate the Mean, Variance, and Standard Deviation**- **Mean**: Multiply each age by its corresponding probability, then sum these values.- **Variance**: Calculate by summing the squared differences between each age and the mean, weighted by their probabilities.- **Standard Deviation**: The square root of the variance.Interpret the results to understand the age distribution of students in the orientation course.

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Description: **Exercise 19: Probability Distribution of Student Ages at Freshman Orientation**The table below represents the ages of students attending a freshman college orientation course:| Age | # of Students ||-----|---------------|| 20 | 6 || 2

(a) Obtain the probability distribution. The probability distribution is obtained below as follows:

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1十9 745 e shows the ages of students at a freshman college orientation course. 21 22 23 24 25 7 16 8. 4 9. obability Distribution -ability Distribution using a Histogram Variance, and Standard Deviation of the Probability Distribution and Interpret

1十9 745 e shows the ages of students at a freshman college orientation course. 21 22 23 24 25 7 16 8. 4 9. obability Distribution -ability Distribution using a Histogram Variance, and Standard Deviation of the Probability Distribution and Interpret

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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**Exercise 19: Probability Distribution of Student Ages at Freshman Orientation**

The table below represents the ages of students attending a freshman college orientation course:

| Age | # of Students |
|-----|---------------|
| 20 | 6 |
| 21 | 7 |
| 22 | 16 |
| 23 | 8 |
| 24 | 4 |
| 25 | 9 |

**a. Construct a Probability Distribution**

To construct the probability distribution, calculate the probability for each age by dividing the number of students of that age by the total number of students.
- Total number of students = 50

**b. Graph the Probability Distribution Using a Histogram**

Create a histogram with the age on the x-axis and the probability on the y-axis. Each bar represents the probability of a student being a certain age.

**c. Calculate the Mean, Variance, and Standard Deviation**

- **Mean**: Multiply each age by its corresponding probability, then sum these values.
- **Variance**: Calculate by summing the squared differences between each age and the mean, weighted by their probabilities.
- **Standard Deviation**: The square root of the variance.

Interpret the results to understand the age distribution of students in the orientation course.

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