REVIEW 4.2 Binomial Distribution

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on an infinite number of values within a given range. For example, the time it takes for a student to complete an exam.

Front

What is the formula to calculate the mean of a binomial distribution?

Back

The mean of a binomial distribution is calculated using the formula: μ = np, where n is the number of trials and p is the probability of success.

Front

What is the formula to calculate the standard deviation of a binomial distribution?

Back

The standard deviation of a binomial distribution is calculated using the formula: σ = √(npq), where q = 1 - p.

Front

What is the probability of getting exactly k successes in n trials in a binomial distribution?

Back

The probability of getting exactly k successes in n trials is given by the formula: P(X = k) = (n choose k) * p^k * q^(n-k), where q = 1 - p.

Front

What does 'n choose k' mean in the context of binomial distribution?

Back

'n choose k' refers to the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

If a binomial distribution has n = 60 and p = 0.7, what is the mean?

Back

The mean is calculated as μ = np = 60 * 0.7 = 42.

Front

What is the relationship between binomial distribution and normal distribution?

Back

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

Front

What is the probability of getting at least one success in a binomial distribution?

Back

The probability of getting at least one success is calculated as 1 - P(X = 0), where P(X = 0) is the probability of zero successes.

Front

What is the variance of a binomial distribution?

Back

The variance of a binomial distribution is calculated using the formula: σ² = npq.

Front

What is the significance of the parameters n and p in a binomial distribution?

Back

In a binomial distribution, n represents the number of trials, and p represents the probability of success on each trial.