Quantitative Analysis- Module 5

True or false: The letter used to denote the standard normal random variable is Z.

True

The inverse transformation, x = μ + zσ is used to ______.

compute x values for given probabilities

The z table used in the textbook provides ___ probabilities.

cumulative

The standard normal distribution is a special case of the___ distribution.

gaussion

The first row of the standard normal table, denoted as the z row, shows values of z up to the ___ decimal point.

hundredths

Scores on the SAT exam follows the___ distributon.

normal

A normal random variable X is transformed into Z by ______.

subtracting the mean, and then dividing by the standard deviation.

The first column of the standard normal table, denoted as the z column, shows values of z up to the __) decimal point.

tenth

We transform X into Z by subtracting from X its mean and dividing by its standard deviation; this is referred to as the standard

transformation

Consider data that are normally distributed. In order to transform a standard normal value z into its unstandardized value x, we use the following formula:

x = μ + zσ

Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula:

z = x−μ/σ

The mean of the standard normal distribution is equal to ______.

zero

The probability that a normal random variable X is less than its mean is equal to

0.50

The shape of the graph depicting the normal probability density function is ______.

bell shaped

The normal distribution is completely described by these two parameters:

mean and variance

Rate of return on an investment follows the ___ distribution.

normal

Since the z table provides the cumulative probabilities for a given value of z, how can we calculate P(Z > z)?

= 1 - P(Z ≤ z)