BSAN Normal Distribution (1-2)

A continuous random variable that can take any real value within its range

What type of random variable follows a normal distribution?

It is symmetric, unimodal, and bell-shaped

What are the three main characteristics of a normal distribution?

The curve becomes wider and flatter because the observations are more spread out.

What happens to a normal distribution when standard deviation increases?

Zero, because a single point has no area under the probability density curve

What is the probability of one exact value in a continuous normal distribution?

A PMF gives probabilities for specific values of a discrete variable. A PDF describes probability density for a continuous variable, where probabilities are areas under the curve.

What is the difference between a PMF and a PDF?

1, or 100%. Because the distribution is symmetric, 50% lies on either side of the mean.

What is the total area under a normal density curve?

A normal distribution with mean 0 and standard deviation 1, written Z - N( 0,1 )

What is a standard normal distribution?

Because the probability of any single exact value is zero, so including the endpoint does not change the probability.

Why are P( X < a ) and P( X ≤ a ) equal for a normal random variable?

A normal distribution with mean 0 and standard deviation 1

What is a standard normal distribution?

How many standard deviations a value is above or below the mean

What does a Z-score measure?

To convert them into standard normal variables so we can calculate probabilities using the Normal Table

Why do we standardize normal random variables?

Equal distances on opposite sides of zero have equal tail probabilities

How does symmetry help with normal probabilities?

Because the probability of any single exact value is zero

Why do strict and inclusive inequalities give the same probabilities for a normal variable?