Normal Distribution Concept in Statistics

These flashcards cover essential concepts related to Normal Distribution and its applications in statistics, focusing on definitions, properties, and theorems presented in the lecture.

What distinguishes a Normal Distribution from other types of distributions?

Normal Distribution is continuous, symmetric, and bell-shaped.

What are the two types of probability distributions?

Discrete Probability Distribution and Continuous Probability Distribution.

What is the significance of the Central Limit Theorem?

As sample size increases, the distribution of sample means approaches a normal distribution.

Define Standard Normal Distribution.

Standard Normal Distribution has a mean of 0 and a standard deviation of 1.

What is the area under the curve (AUC) in Standard Normal Distribution used for?

AUC represents the probability.

Provide the properties of Normal Distribution.

Bell-shaped, unimodal, mean=median=mode, area under the curve is 1.

What does a Z-score represent?

A Z-score indicates how many standard deviations an element is from the mean.

What percentage of data lies within 1 standard deviation of the mean in a normal distribution?

Approximately 68% of data.

What is a random variable?

A variable whose values are determined by chance.

Explain the importance of understanding Probability Distribution.

It helps in quantifying uncertainty and data analysis.

What are the specific percentages for the Empirical Rule beyond 68%?

Approximately 95\% of data falls within 2 standard deviations, and 99.7\% falls within 3 standard deviations of the mean.

What is the mathematical formula for a Z-score?

The formula is z = \frac{x - \mu}{\sigma} where x is the value, \mu is the mean, and \sigma is the standard deviation.

How does the standard deviation (\sigma) affect the shape of the normal curve?

A smaller standard deviation makes the curve taller and narrower, while a larger standard deviation makes it shorter and wider.

Where do the points of inflection occur in a normal distribution?

The points of inflection occur exactly one standard deviation away from the mean, at \mu + \sigma and \mu - \sigma.

Describe the probability of a single point in a continuous distribution.

The probability that a continuous random variable equals a specific value is always 0 because probability corresponds to the area under the curve over an interval.