Normal Approximation in Statistics

The video tutorial explains the normal approximation to the binomial distribution, highlighting its historical significance and current applications in statistical inference. It discusses the conditions under which the normal approximation is most effective, particularly when the binomial distribution is symmetric and the sample size is large. The tutorial covers the process of standardizing a binomial random variable to a Z-score and demonstrates probability calculations using the normal approximation. It also introduces the concept of continuity correction to improve approximation accuracy when transitioning from discrete to continuous distributions.

Why was the normal approximation to the binomial distribution historically significant?

• It was easier to understand than the binomial formula.

• It simplified complex probability calculations.

• It was the only method available for probability calculations.

• It provided exact results for all probability calculations.

When does the normal approximation work best for a binomial distribution?

• When p is exactly 0.5 and the sample size is small.

• When p is close to 0.5 and the sample size is large.

• When p is close to 0 or 1 and the sample size is small.

• When p is exactly 0.5 regardless of sample size.

What happens to the normal approximation as the sample size increases?

• It becomes irrelevant.

• It becomes more accurate.

• It remains the same.

• It becomes less accurate.

What is the guideline for using the normal approximation regarding n * p?

• n * p should be less than or equal to 5.

• n * p should be greater than or equal to 10.

• n * p should be exactly 10.

• n * p should be less than 10.

How is the binomial distribution standardized for normal approximation?

• By subtracting the mean and dividing by the standard deviation.

• By dividing by the mean.

• By adding the mean and variance.

• By multiplying by the variance.

What is the approximate probability that Zed is greater than or equal to 1.645?

• 0.495

• 0.611

• 0.385

• 0.628

What is the purpose of continuity correction in normal approximation?

• To simplify the calculation process.

• To eliminate the need for standard deviation.

• To improve the approximation by adjusting for discreteness.

• To make the approximation less accurate.

When using continuity correction, where should you start for a probability that X is greater than or equal to 52?

• At 53

• At 52.5

• At 51.5

• At 50