Define binomial distribution.
A probability distribution for a fixed number of trials, each with two possible outcomes.
True or false: The normal distribution is symmetric about its mean.
TRUE
The normal distribution is often referred to as a bell curve.
What does Z score represent?
The number of standard deviations a data point is from the mean.
Fill in the blank: In a binomial distribution, the probability of success is denoted by ______.
p
What is the mean of a binomial distribution?
The mean is calculated as n * p, where n is the number of trials.
True or false: The sum of probabilities in a binomial distribution equals 1.
TRUE
Define standard normal distribution.
A normal distribution with a mean of 0 and a standard deviation of 1.
What is the variance of a binomial distribution?
The variance is calculated as n * p * (1 - p).
Fill in the blank: The Central Limit Theorem states that the sampling distribution of the mean approaches ______.
a normal distribution as sample size increases.
What is the standard deviation of a normal distribution?
A measure of the dispersion of data points around the mean.
True or false: A Z score of 0 indicates a value at the mean.
TRUE
Define success in the context of a binomial experiment.
An outcome that corresponds to the event of interest in the trials.
What is the probability mass function for a binomial distribution?
It gives the probability of obtaining exactly k successes in n trials.
Fill in the blank: The area under the curve of a normal distribution equals ______.
1
What does a negative Z score indicate?
The value is below the mean of the distribution.
True or false: The binomial distribution can model continuous data.
FALSE
The binomial distribution is discrete, suitable for count data.
Define binomial experiment.
An experiment with a fixed number of independent trials, each with two outcomes.
What is the cumulative distribution function for a binomial distribution?
It gives the probability of obtaining up to k successes in n trials.
Fill in the blank: In a normal distribution, about 68% of values lie within ______ standard deviations of the mean.
1
What is the law of large numbers?
As the number of trials increases, the sample mean converges to the expected value.
