Stats Chapter 6: Continuous Probability Distributions

The probability that a normal random variable with mean μ and standard deviation σ falls in between μ - 2σ and μ + 2σ is

0.9544

which of the following is not a characteristic of normal distributions?

both tails of a normal curve (normal density function) are asymptotical in the sense that they approach the horizontal axis and touch it

A random variable that assumes any value from an interval (or collection of intervals) is called

continuous

the function that defines the probability distribution of a continuous random variable is a

probability density function

which of the following random variables is not continuous (is discrete)

the number of arrivals to a bank in a two hour period

a normal distribution with a mean of 0 and a standard deviation of 1 is called

the standard normal distribution (the z distribution)

Any normal variable with mean μ and standard deviation σ can be converted into the standard normal variable by the following transformation

z = (x - μ)/σ

A continuous random variable with the uniform distribution on an interval [a,b] satisfies the following:

all of the above (the probability that it assumes a particular value is zero; its density function is constant for any value from [a,b]; for all subintervals of [a,b] with equal length, the probability of taking a value from the subinterval is the same)