Podcast
Questions and Answers
Which of the following describes a random variable?
Which of the following describes a random variable?
- A variable whose values are constant.
- A variable with only infinite possible values.
- A variable whose values are determined by chance. (correct)
- A variable that cannot be modified.
Which statement accurately describes a discrete variable?
Which statement accurately describes a discrete variable?
- It has a finite or countably infinite number of values. (correct)
- Its values include all fractions and decimals.
- Its values are measured, not counted.
- It can assume all values in an interval.
Which of the following is an example of a discrete variable?
Which of the following is an example of a discrete variable?
- The number of cars passing a point on a highway in an hour. (correct)
- The temperature of a room.
- The weight of apples in a basket.
- The height of students in a class.
What characteristic defines a continuous variable?
What characteristic defines a continuous variable?
Which of the following is an example of a continuous variable?
Which of the following is an example of a continuous variable?
A variable represents the number of houses in a neighborhood. What type of variable is this?
A variable represents the number of houses in a neighborhood. What type of variable is this?
The time it takes to run a mile is recorded for a track team. What type of variable is this?
The time it takes to run a mile is recorded for a track team. What type of variable is this?
Which of the following accurately describes a discrete probability distribution?
Which of the following accurately describes a discrete probability distribution?
A discrete probability distribution of a fair six-sided die is made. What is the probability of rolling any single number?
A discrete probability distribution of a fair six-sided die is made. What is the probability of rolling any single number?
Which step is essential when constructing a discrete probability distribution?
Which step is essential when constructing a discrete probability distribution?
If constructing a graph for a discrete probability distribution, what should be placed on the x-axis?
If constructing a graph for a discrete probability distribution, what should be placed on the x-axis?
In a discrete probability distribution, if each outcome is equally likely, and there are 5 possible outcomes, what is the probability of each outcome?
In a discrete probability distribution, if each outcome is equally likely, and there are 5 possible outcomes, what is the probability of each outcome?
What must the sum of the probabilities of all events in a sample space equal for it to be a valid probability distribution?
What must the sum of the probabilities of all events in a sample space equal for it to be a valid probability distribution?
In a probability distribution, what range must the probability of each event fall within?
In a probability distribution, what range must the probability of each event fall within?
A survey of high school students is conducted, and the number of pets they have is recorded. The results are as follows: 5 students have 0 pets, 4 have 1 pet, 6 have 2 pets, 8 have 3 pets, 1 has 4 pets and 1 has 5 pets. If a student is selected at random, determine the probability they have at least 3 pets.
A survey of high school students is conducted, and the number of pets they have is recorded. The results are as follows: 5 students have 0 pets, 4 have 1 pet, 6 have 2 pets, 8 have 3 pets, 1 has 4 pets and 1 has 5 pets. If a student is selected at random, determine the probability they have at least 3 pets.
Given the formula for the mean of a probability distribution $μ = ΣX \cdot P(X)$, what does $P(X)$ represent?
Given the formula for the mean of a probability distribution $μ = ΣX \cdot P(X)$, what does $P(X)$ represent?
What does $σ^2$ represent in the formula for variance of a probability distribution, $σ^2 = Σ[X^2 \cdot P(X)] - μ^2$?
What does $σ^2$ represent in the formula for variance of a probability distribution, $σ^2 = Σ[X^2 \cdot P(X)] - μ^2$?
How is the standard deviation (σ) related to the variance ($σ^2$) in a probability distribution?
How is the standard deviation (σ) related to the variance ($σ^2$) in a probability distribution?
Which of the following statements accurately describes a normal distribution?
Which of the following statements accurately describes a normal distribution?
In a standard normal distribution, what is the mean and standard deviation?
In a standard normal distribution, what is the mean and standard deviation?
What does the Z-score measure?
What does the Z-score measure?
If value = 80, mean = 70, and standard deviation = 5, what is the Z-score?
If value = 80, mean = 70, and standard deviation = 5, what is the Z-score?
What is the appropriate action when calculating probabilities to the left of a z-score using a standard Z-table?
What is the appropriate action when calculating probabilities to the left of a z-score using a standard Z-table?
What adjustment is necessary when determining probabilities for a Z-score 'to the right'?
What adjustment is necessary when determining probabilities for a Z-score 'to the right'?
How do you calculate the probability between two z-scores, z1 and z2?
How do you calculate the probability between two z-scores, z1 and z2?
If a data set follows a normal distribution, approximately what percentage of the data falls within one standard deviation of the mean?
If a data set follows a normal distribution, approximately what percentage of the data falls within one standard deviation of the mean?
To apply the Central Limit Theorem, under what conditions must samples be drawn from a population?
To apply the Central Limit Theorem, under what conditions must samples be drawn from a population?
How does increasing the sample size generally affect the standard error of the mean?
How does increasing the sample size generally affect the standard error of the mean?
A polling organization is trying to predict an election. They survey 500 likely voters. Given this is a normal distribution, what does the standard error represent?
A polling organization is trying to predict an election. They survey 500 likely voters. Given this is a normal distribution, what does the standard error represent?
Flashcards
Variable
Variable
A characteristic or attribute that can assume different values.
Random Variable
Random Variable
A variable whose values are determined by chance.
Discrete Variable
Discrete Variable
A variable with a finite number of possible values or an infinite number of values that can be counted.
Continuous Variable
Continuous Variable
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Discrete Probability Distribution
Discrete Probability Distribution
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Normal Distribution
Normal Distribution
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Standard Normal Distribution
Standard Normal Distribution
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Z-score
Z-score
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Study Notes
Math 11 3rd QTR Review
- The review covers random variables and probability distributions, including discrete and normal distributions.
- The slides should be reviewed and sample problems solved.
Random Variables and Probability Distribution
- Variable: A characteristic or attribute that can assume different values.
- Random Variable: A variable whose values are determined by chance.
- Discrete Variable: Has a finite number of possible values or an infinite number of countable values, and can be identified individually.
- Enumerated using numbers like 1, 2, 3, etc.
- Number of letters in a word is an example.
- Continuous Variable: It can be measured at any level of precision, like temperature or height.
- Can assume all values in an interval between any two given values.
- Obtained from data that can be measured rather than counted and can assume infinite decimal/fractional values.
- Height, weight, temperature, and time are examples.
Discrete Probability Distribution
- Consists of the values a random variable can assume and the corresponding probabilities of the values.
- The probabilities are determined theoretically or by observation.
- A way of listing all possible outcomes of a random event and the probability of each outcome.
- When a six-sided die is rolled, the possible numeric outcomes are 1, 2, 3, 4, 5, and 6, the die roll can assume.
- The probability chances of each number showing up on the die are all 1/6 on a fair die.
Constructing a Probability Distribution
- Create a frequency distribution for the outcomes of the variable
- Find the probability for each outcome by dividing the frequency of the outcome by the frequencies' sum.
- Place the outcomes on the x-axis and the probabilities on the y-axis for a graph.
- Vertical bars should then be drawn for each outcome with its corresponding probability.
- Two Requirements for a Probability Distribution:
- The probabilities sum should = 1
- The probability of each event should lie between 0 and 1.
Formula for Mean of Probability Distribution
- μ = ΣX • P(X), where outcomes are X₁, X₂, ..., Xn and corresponding probabilities are P(X₁), P(X₂), P(X3),..., P(Xn).
Formula for Variance of Probability Distribution
- σ² = Σ [X² • P(X)] – μ²
Standard Deviation Formula
- σ = √σ²
Normal Distribution
- Defined as a continuous, bell-shaped, and symmetric probability distribution.
- Describes a set of data that clusters around a central value without bias.
Standard Normal Distribution
- Normal distribution with a mean of 0 and a standard deviation of 1.
Z-Score Formula
- z = (value - mean) / standard deviation
- z = (X - μ) / σ
Z-Score Key
- 'Z' To the left = as is
- 'Z' To the right = 1-z
- 'Z' Between = z2 - z1
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Description
Review of random variables and probability distributions for Math 11, focusing on discrete and normal distributions. Study the slides and work through sample problems to prepare. Key topics include discrete and continuous variables.
