Chapter 6 Practice AP Test

Front

What does the standard deviation of a probability distribution represent?

Back

The standard deviation indicates how much the values of a random variable typically differ from the mean.

Front

What is the definition of independent random variables?

Back

Two random variables are independent if the occurrence of one does not affect the probability of the occurrence of the other.

Front

How do you calculate the mean of a total revenue random variable from a sales scenario?

Back

Multiply the mean number of items sold by the price per item.

Front

What is a binomial distribution?

Back

A binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is the formula for the mean of a binomial distribution?

Back

The mean (μ) 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 standard deviation of a binomial distribution?

Back

The standard deviation (σ) of a binomial distribution is calculated as σ = √(n * p * (1 - p)).

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, defined by its mean and standard deviation.

Front

How does the Central Limit Theorem relate to normal distributions?

Back

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the original distribution.

Front

What is the relationship between the mean and standard deviation of a sum of independent random variables?

Back

The mean of the sum is the sum of the means, and the variance of the sum is the sum of the variances.

Front

What is the significance of the area under the probability distribution curve?

Back

The area under the probability distribution curve represents the total probability, which equals 1.