ISDS 2000 - Chapter 6

The Gaussian

- The normal probability distribution, or simply the normal distribution - Normal bell shaped curve (mean = median = mode)

The standard normal table is also referred to as what?

A Z table!

Which of the following random variables is depicted with a bell-shaped curve?

A normal random variable

The probability that the normal random variable Z is less than 1.5 is equal to?

P(Z > -1.5)

When approximating the binomial distribution using the normal distribution, what value is used for the standard deviation?

Square root of np(1-p)

What does "cumulative probability" mean?

The probability that Z is less than or equal to a given z value

The standard normal random variable zZ is a normal variable with E(Z) = ______ and SD(Z) = ________

Zero and One

The z table used in the textbook provides _______ probabilities

cumulative

Due to symmetry, the probability that the standard normal random variable Z is greater than 0 is

equal to 0.5

The normal distribution is completely described by these two parameters:

mean and variance

You use R's _______ function to find probabilities associated with the normal distribution

qnorm

If X is normally distributed random variable, then

the mean, median, and mode are all equal

We transform X into Z by subtracting from X its mean and dividing by its standard deviation, that is referred to as.....

tranformation

In order to transform a standard normal value z into its unstandardized value x, we use the following formula.....

x = μ + zσ

In order to transform a value x into it standardized value z, we use the formula....

z = (x−μ)/σ