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Questions and Answers
What is the range of movie lengths in the scenario described in question 1?
What is the range of movie lengths in the scenario described in question 1?
80 minutes to 125 minutes
What is the probability that a randomly selected movie will run for less than 95 minutes?
What is the probability that a randomly selected movie will run for less than 95 minutes?
$rac{15}{45} = rac{1}{3}$
What is the notation used to describe a normal distribution with a mean of 25 and a standard deviation of 2.5?
What is the notation used to describe a normal distribution with a mean of 25 and a standard deviation of 2.5?
X ~ N(25, 2.5)
What is the condition for approximating a binomial distribution with a normal distribution?
What is the condition for approximating a binomial distribution with a normal distribution?
Determine the probability that a student randomly selected from the class will have a test score between 69% and 81%.
Determine the probability that a student randomly selected from the class will have a test score between 69% and 81%.
What is the probability that a student randomly selected from the class will have a test score greater than 88%?
What is the probability that a student randomly selected from the class will have a test score greater than 88%?
What is the shape of the graph for a continuous uniform distribution?
What is the shape of the graph for a continuous uniform distribution?
What is the mean of a normal distribution described as X ~ N(25, 2.5)?
What is the mean of a normal distribution described as X ~ N(25, 2.5)?
Flashcards
Movie Length Range
Movie Length Range
Movie lengths range from 80 to 125 minutes.
Probability < 95 min
Probability < 95 min
15 out of 45 movies are shorter than 95 minutes = 1/3 probability.
Normal Dist. Notation
Normal Dist. Notation
X ~ N(25, 2.5) describes a normal distribution with mean 25 and standard deviation 2.5.
Binomial Normal Approx
Binomial Normal Approx
Approximating a binomial with a normal distribution requires np >= 5 and n(1-p) >= 5.
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Test Score (69-81%)
Test Score (69-81%)
Probability is ~0.6827 for scores between 69% and 81%.
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Test Score > 88%
Test Score > 88%
Probability is ~0.1587 for scores above 88%.
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Uniform Dist. Shape
Uniform Dist. Shape
A continuous uniform distribution has a rectangular graph shape.
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Normal Mean
Normal Mean
The mean of a normal distribution X ~ N(25, 2.5) is 25.
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Movie Lengths
Movie Lengths
A range of movie lengths between 80 and 125 minutes.
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Probability Calculation
Probability Calculation
Calculating probabilities involving fractions of movies, or event occurrence in a set.
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Normal Distribution
Normal Distribution
A bell-shaped probability distribution.
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Binomial Distribution
Binomial Distribution
Probability distribution of a binomial experiment.
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Standard Normal Distribution
Standard Normal Distribution
A normal distribution with mean 0 and standard deviation 1.
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Continuous Uniform Distribution
Continuous Uniform Distribution
Probability distribution where all values in a given range are equally likely.
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Mean
Mean
The average value.
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Continuous Probability Distributions
Uniform Distribution
- A uniform distribution is a continuous probability distribution where every possible value has an equal chance of being selected.
- Example: movie lengths ranging evenly between 80 minutes and 125 minutes.
- Graph: rectangular shape with equal heights and widths.
Normal Distribution
- A normal distribution is a continuous probability distribution that is symmetric and bell-shaped.
- Parameters: mean (μ) and standard deviation (σ).
- Example: test scores with a mean of 25 and a standard deviation of 2.5.
- Notation: X ~ N(μ, σ)
- Graph: bell-shaped curve with mean at the center and standard deviation marking the spread.
Approximating Binomial Distributions with Normal Distributions
- A binomial distribution can be approximated using a normal distribution if:
- n (number of trials) is large (> 30).
- p (probability of success) is close to 0.5.
- Examples:
- n = 50, p = 0.92: can be approximated using normal distribution.
- n = 75, p = 0.2: can be approximated using normal distribution.
- n = 25, p = 0.4: cannot be approximated using normal distribution.
Calculating Probabilities with Normal Distributions
- To calculate the probability of an event, find the z-score and use a standard normal distribution table or calculator.
- Example: test scores with a mean of 75% and a standard deviation of 6%.
- Probability of a score between 69% and 81%: find z-scores and calculate probability.
- Probability of a score greater than 88%: find z-score and calculate probability.
- Graph: sketch the normal distribution curve and shade the desired area.
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