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Questions and Answers
Which of the following is the correct 95% confidence interval for the true population proportion?
Which of the following is the correct 95% confidence interval for the true population proportion?
- C. $p \pm 1.96\sigma(p)$ (correct)
- A. $\mu \pm 1.96\sigma(p)$
- D. $\mu \pm 1.0\sigma(p)$
- B. $p \pm 1.0\sigma(p)$
What is the probability that a 5 appears on the first dice if the sum of the two die faces is 9 or greater?
What is the probability that a 5 appears on the first dice if the sum of the two die faces is 9 or greater?
- B. 4/5
- D. 1/2 (correct)
- C. 3/5
- A. 3/10
How many combinations will be used for each cooking time if there are 3 different temperatures, 4 different cooking times, and 3 different oils?
How many combinations will be used for each cooking time if there are 3 different temperatures, 4 different cooking times, and 3 different oils?
- A. 9
- D. 24
- C. 12
- B. 36 (correct)
An urn is selected at random and a marble is drawn. If the probability of selecting Urn A is 1/3, Urn B is 1/2, and Urn C is 1/6, what is the probability of drawing a red marble?
An urn is selected at random and a marble is drawn. If the probability of selecting Urn A is 1/3, Urn B is 1/2, and Urn C is 1/6, what is the probability of drawing a red marble?
If the sum of the two die faces is 9 or greater, what is the probability that the first dice shows a 5?
If the sum of the two die faces is 9 or greater, what is the probability that the first dice shows a 5?
Flashcards
95% Confidence Interval for Proportion
95% Confidence Interval for Proportion
The range of values within which the true population proportion is likely to fall, given the observed sample proportion.
Probability of 5 (sum ≥ 9)
Probability of 5 (sum ≥ 9)
The chance that the first die shows a 5, given the sum of two dice is 9 or greater.
Combinations (3 temps, 4 times, 3 oils)
Combinations (3 temps, 4 times, 3 oils)
The total number of possible cooking combinations given choices of temperature, time, and oil.
Probability of Red Marble
Probability of Red Marble
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Probability of 5 (sum ≥ 9)
Probability of 5 (sum ≥ 9)
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Study Notes
Confidence Intervals
- A 95% confidence interval estimates the range where the true population proportion is likely to fall.
- Calculation typically involves sample proportion, standard error, and Z-scores associated with desired confidence level.
Probability with Dice
- To find the probability of rolling a 5 on the first die, given that the sum of two dice is 9 or greater, consider valid combinations.
- Valid combinations for a sum of 9 or greater include (5,4), (6,3), (7,2), (8,1), (4,5), (3,6), (2,7), (1,8) and so forth.
Combinations of Cooking Time
- Total combinations factor in various cooking times, temperatures, and oils.
- Possible combinations formula: number of temperatures x number of cooking times x number of oils.
- For parameters: 3 temperatures, 4 cooking times, and 3 types of oil results in 36 unique combinations.
Probability of Drawing from Urns
- Probability of selecting an urn influences the likelihood of drawing a red marble.
- For Urn A (1/3), Urn B (1/2), Urn C (1/6), calculation for a red marble requires knowing how many red marbles are in each urn.
Conditional Probability of Dice
- The probability of getting a 5 on the first die follows specific conditions when the total is at least 9.
- Valid scenarios must be analyzed to determine what fraction of total outcomes produces a 5 on the first die.
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