Statistics Probability & Distributions 2 — Questions and Answers
Question 1: For a standard normal distribution, what is the mean and standard deviation?
- Mean = 0, SD = 1 (Correct answer)
- Mean = 1, SD = 0
- Mean = 0.5, SD = 0.5
- Mean = 1, SD = 1
Correct answer: Mean = 0, SD = 1
The standard normal distribution Z is defined by a mean of 0 and a standard deviation of 1.
Question 2: What is the relationship between the mean and variance of a binomial distribution with parameters n and p?
- Mean = np, Variance = np(1−p) (Correct answer)
- Mean = np, Variance = np
- Mean = p, Variance = np
- Mean = np², Variance = np
Correct answer: Mean = np, Variance = np(1−p)
For a binomial distribution, mean equals np and variance equals np(1−p).
Question 3: Which of the following describes a continuous uniform distribution on [a, b]?
- All values between a and b are equally likely (Correct answer)
- Only integer values between a and b are possible
- Values cluster around the midpoint
- The distribution has a bell shape
Correct answer: All values between a and b are equally likely
A continuous uniform distribution assigns equal probability density to every value in the interval [a, b].
Question 4: Bayes' theorem allows you to update which quantity?
- The probability of a hypothesis given new evidence (Correct answer)
- The sample size required for a study
- The critical value for a hypothesis test
- The variance of a population
Correct answer: The probability of a hypothesis given new evidence
Bayes' theorem calculates posterior probability by combining a prior probability with the likelihood of observed evidence.
Question 5: What is the probability that a randomly selected value from a normal distribution falls more than 1.96 standard deviations from the mean?
- 0.05 (Correct answer)
- 0.025
- 0.95
- 0.10
Correct answer: 0.05
Approximately 95% of a normal distribution falls within 1.96 standard deviations, leaving 5% in the tails.
Question 6: What distinguishes a discrete probability distribution from a continuous one?
- Discrete distributions assign probability to countable individual values (Correct answer)
- Discrete distributions always follow a bell shape
- Continuous distributions have a finite number of outcomes
- Discrete distributions have a mean of zero
Correct answer: Discrete distributions assign probability to countable individual values
Discrete distributions assign positive probability to each countable outcome, while continuous distributions use probability density.
Statistics Probability & Distributions 2
For a standard normal distribution, what is the mean and standard deviation?