Normal Approximation to a binomial distribution

Front

What is the normal approximation to a binomial distribution?

Back

The normal approximation to a binomial distribution is a method used to approximate the probabilities of a binomial random variable using a normal distribution when certain conditions are met.

Front

What are the conditions for using the normal approximation to a binomial distribution?

Back

The normal approximation is appropriate when both np and nq are greater than 5, where n is the number of trials, p is the probability of success, and q is the probability of failure (q = 1 - p).

Front

What is the continuity correction factor?

Back

The continuity correction factor is a value added or subtracted (usually 0.5) when using a normal distribution to approximate a discrete distribution, to account for the fact that the normal distribution is continuous.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the mean (μ) of a binomial distribution?

Back

The mean (μ) 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

How do you calculate the variance (σ²) of a binomial distribution?

Back

The variance (σ²) of a binomial distribution is calculated using the formula σ² = npq, where n is the number of trials, p is the probability of success, and q is the probability of failure.

Front

What is the standard deviation (σ) of a binomial distribution?

Back

The standard deviation (σ) of a binomial distribution is the square root of the variance, calculated as σ = √(npq).

Front

If 46% of a population favors a candidate, what is the probability of selecting a sample of 500 that favors the candidate?

Back

Using the normal approximation, calculate the probability using the mean and standard deviation derived from the binomial parameters.

Tags

CCSS.HSS.ID.A.4

Front

What is the probability of finding more than 60 vehicles with undeclared goods in a sample of 500 if 10% carry undeclared goods?

Back

Use the normal approximation to calculate the probability, applying the continuity correction factor.

Tags

CCSS.HSS.ID.A.4

Front

What does it mean if np and nq are less than 5 in a binomial distribution?

Back

If np and nq are less than 5, the normal approximation may not be valid, and the binomial distribution should be used instead.

Tags

CCSS.HSS.ID.A.4

Front

For which binomial distribution is the normal approximation not reasonable?

Back

The normal approximation is not reasonable for n = 40, p = 0.12, as np and nq are both less than 5.