Statistics Probability & Distributions 2

Question 1

For a standard normal distribution, what is the mean and standard deviation?

Accepted Answer

Mean = 0, SD = 1

Answer

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?

Accepted Answer

Mean = np, Variance = np(1−p)

Answer

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]?

Accepted Answer

All values between a and b are equally likely

Answer

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?

Accepted Answer

The probability of a hypothesis given new evidence

Answer

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?

Accepted Answer

0.05

Answer

Approximately 95% of a normal distribution falls within 1.96 standard deviations, leaving 5% in the tails.

Statistics Practice Test