Statistics Ch 4 Practice Test

Front

What is the expected value in probability and statistics?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability of occurrence.

Front

How do you calculate the expected number of trials until the first success in a geometric distribution?

Back

The expected number of trials until the first success is given by E(X) = 1/p, where p is the probability of success.

Front

What is the formula for calculating the probability of a specific outcome in a binomial distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

Front

What is the significance of the mean and standard deviation in a normal distribution?

Back

The mean indicates the center of the distribution, while the standard deviation measures the spread or dispersion of the data around the mean.

Front

What is the probability of not picking the correct number in a game of roulette until the fifth try?

Back

The probability can be calculated using the formula (1 - p)^(k-1) * p, where p is the probability of success on each trial.

Front

How do you find the mean of a binomial distribution?

Back

The mean of a binomial distribution is calculated as μ = n * p, where n is the number of trials and p is the probability of success.

Front

What is the relationship between odds and probability?

Back

Odds represent the ratio of the probability of an event occurring to the probability of it not occurring, expressed as odds = p / (1 - p).

Front

What is a fair die, and how does it affect expected value calculations?

Back

A fair die has an equal probability of landing on any of its faces, which means each outcome has a probability of 1/6, affecting the expected value calculations accordingly.

Front

What does it mean for events to be independent in probability?

Back

Two events are independent if the occurrence of one does not affect the probability of the other occurring.

Front

How do you calculate the standard deviation for a binomial distribution?

Back

The standard deviation is calculated as σ = √(n * p * (1 - p)), where n is the number of trials and p is the probability of success.