Questions and Answers
What is the expected profit in dollars?
Var(X - Y) = Var(X) + Var(Y) is true for independent random variables X and Y.
True
What is P(X > $400 if X is normally distributed with mean $360 and standard deviation $50?
Which of the following best describes the setting when selecting red cards from a deck?
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What are the mean (μ) and standard deviation (σ) of the number of students who have experienced math anxiety from a sample of 10 students?
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Which of the following statements is true?
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Study Notes
Expected Profit Calculation
- Expected profit for the business venture calculated using the formula: ( E(X) = \sum (X_i \cdot P(X_i)) )
- Profits and their probabilities:
- $10,000 profit with probability ( \frac{3}{20} )
- $5,000 profit with probability ( \frac{9}{20} )
- $0 profit with probability ( \frac{5}{20} )
- $5,000 loss with probability ( \frac{3}{20} )
- Resulting expected profit equals $3,000.
Variance of Independent Variables
- For independent random variables X and Y, the variance of their difference is given by:
- ( \text{Var}(X - Y) = \text{Var}(X) + \text{Var}(Y) )
Normal Distribution Problem
- For normally distributed random variable X with mean $360 and standard deviation $50, to find:
- ( P(X > 400) )
- Calculated probability results in approximately 0.2119.
Binomial Distribution in Card Selection
- Random variable Y (number of red cards in 40 drawn from a deck) best modeled with:
- Binomial distribution with ( n = 40 ) and probability of success ( p = 0.5 ), under the condition of card replacement and shuffling after each selection.
Sample Mean and Standard Deviation for Math Anxiety
- In a population where 20% of college students experience math anxiety, for a sample of 10 students:
- Mean number ( \mu ) of students with anxiety is 2.
- Standard deviation ( \sigma ) calculated as ( \sqrt{10 \times 0.2 \times 0.8} ), which equals approximately 1.265.
Differences Between Binomial and Geometric Settings
- Binomial setting allows for a fixed number of trials with two possible outcomes; geometric setting permits a variable number of trials.
- In a geometric random variable, the number of successes is not capped, differing fundamentally from the binomial model.
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Description
Test your understanding of Chapter 6 in AP Statistics with these multiple choice questions. This quiz covers key concepts related to probability and expected values in statistics. Perfect for review before exams or as a study aid.
