Podcast
Questions and Answers
A student guesses the answer to every question. Let X be the number of correct answers. They will expect to get ______ correct.
A student guesses the answer to every question. Let X be the number of correct answers. They will expect to get ______ correct.
mu
The probability of winning a prize in a game of chance is ______.
The probability of winning a prize in a game of chance is ______.
0.35
In a sample of n children, 70% said yes to using social media. The sample proportion p ̂ is ______.
In a sample of n children, 70% said yes to using social media. The sample proportion p ̂ is ______.
0.7
The heights of the class of 2024 are normally distributed with an average of ______ cm.
The heights of the class of 2024 are normally distributed with an average of ______ cm.
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60% of students catch public transportation to school. That day, the probability that at least one of the selected students caught public transport is ______.
60% of students catch public transportation to school. That day, the probability that at least one of the selected students caught public transport is ______.
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The probability that a full forward will kick a goal is ______.
The probability that a full forward will kick a goal is ______.
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If there are 74 students in the cohort, we would expect ______ of them to be shorter than 168cm.
If there are 74 students in the cohort, we would expect ______ of them to be shorter than 168cm.
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The standard deviation of the heights in the class is ______ cm.
The standard deviation of the heights in the class is ______ cm.
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The probability function f(x) for the continuous random variable X is given as f(x) = {█(k______(4-x),0≤x≤4@@0, otherwise).
The probability function f(x) for the continuous random variable X is given as f(x) = {█(k______(4-x),0≤x≤4@@0, otherwise).
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In a particular city, it was surveyed that ______% of people have a driver’s license.
In a particular city, it was surveyed that ______% of people have a driver’s license.
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15% of coke cans have less than ______ mL of coke.
15% of coke cans have less than ______ mL of coke.
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The mean and standard deviation of the amount of coke in a coke can are found using the ______ distribution.
The mean and standard deviation of the amount of coke in a coke can are found using the ______ distribution.
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A survey showed that 237 from a random sample of ______ answered yes to a certain question.
A survey showed that 237 from a random sample of ______ answered yes to a certain question.
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The confidence intervals for the proportion of undergraduates are calculated at ______%, 95%, and 99%.
The confidence intervals for the proportion of undergraduates are calculated at ______%, 95%, and 99%.
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Study Notes
Question 1: Probability and Expected Values
- Exam consists of 30 multiple-choice questions with 3 possible answers each.
- If a student guesses, the expected number of correct answers, E(X) or μ, is calculated as (μ = \frac{1}{3} \times 30 = 10).
- Variance, Var(X), can be computed using the formula for a binomial distribution: (Var(X) = n \cdot p \cdot (1 - p) = 30 \cdot \frac{1}{3} \cdot \frac{2}{3} = 20).
- Standard deviation is the square root of variance: (SD(X) = \sqrt{Var(X)} = \sqrt{20} \approx 4.47).
Question 2: Probability in Games of Chance
- Winning probability in a game is 0.35.
- Aim is to find the minimum number of games to play for winning at least twice with a probability greater than 0.9.
Question 3: Sample Proportion and Margin of Error
- A survey indicates 70% of primary school children use social media.
- Sample proportion (p̂ = 0.70).
- Margin of error (E) at 95% confidence level is expressed as (E = z \cdot \sqrt{\frac{p̂(1 - p̂)}{n}}), where (z) corresponds to the z-value for 95% confidence.
- Tripling the sample size (n) reduces the margin of error (E) by about 29%.
Question 4: Normal Distribution of Heights
- Heights in a class are normally distributed with mean 175 cm and standard deviation 6 cm.
- To find the expected number of students shorter than 168 cm, utilize the z-score formula and the normal distribution table.
Question 5: Probability with Public Transport
- 60% of students use public transport; random selection of 4 students.
- Probability that at least one student caught public transport can be found using (P(X ≥ 1) = 1 - P(X = 0)).
Question 6: Probability of Kicking Goals in AFL
- Probability of a goal for a full forward is 0.15 with 10 kicks.
- Compute probabilities for:
- Kicking a goal every time: (P(X = 10) = (0.15)^{10}).
- Kicking at least one goal: Use complementary probability.
- Kicking more than one goal given at least one goal: Conditional probability (P(X > 1 | X ≥ 1)).
Question 7: Continuous Random Variable
- (f(x) = kx(4 - x)) for (0 ≤ x ≤ 4), find value of constant (k).
- Calculate expected value (E(X)) using the probability function.
Question 8: Driver's License Probability
- 60% of surveyed individuals have a driver's license.
- Approximate probability for more than 65% of a sample of 200 people using normal approximation to the binomial distribution.
Question 9: Normal Distribution of Coke Cans
- 15% of cans < 372 mL, and 10% > 379 mL.
- Find mean and standard deviation of coke amount in a can.
- To determine the proportion of cans with less than 377 mL, use the derived normal distribution parameters.
Question 10: Confidence Intervals for Postgraduate Intent
- Survey of 500 individuals shows 237 want to pursue postgraduate studies.
- Calculate confidence intervals for proportions at 90%, 95%, and 99% levels, comparing the intervals statistically.
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Description
Test your understanding of probability concepts and expected values with this engaging quiz. Covering topics from multiple-choice guessing to games of chance and sample proportions, this quiz will challenge your grasp on statistical measures. Perfect for students looking to enhance their skills in probability theory.
