Binomial and Normal Distributions Review

Front

What is the mean of a binomial distribution with parameters n and p?

Back

Mean (μ) = n * p

Front

What is the probability of getting less than k successes in a binomial distribution?

Back

Use the binomial probability formula or cumulative distribution function.

Front

Define a continuous random variable.

Back

A variable that can take any value within a given range.

Front

What is a probability distribution?

Back

A function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

What are the conditions for a valid probability distribution?

Back

1. All probabilities P(x) must be between 0 and 1. 2. The sum of all probabilities must equal 1.

Front

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

Back

Standard Deviation (σ) = √(n * p * (1 - p))

Front

What is the normal distribution?

Back

A continuous probability distribution characterized by a symmetric bell-shaped curve.

Front

What is the empirical rule in statistics?

Back

Approximately 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations from the mean.

Front

How do you find the middle 60% of a normal distribution?

Back

Identify the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.

Front

What is the relationship between binomial and normal distributions?

Back

The binomial distribution can be approximated by the normal distribution when n is large and p is not too close to 0 or 1.