Chapter 6 assign.

A random variable X with an equally likely chance of assuming any value within a specified range is said to have which distribution?

continuous uniform distribution

The mean and variance of the standard normal distribution are ______, respectively.

0 and 1

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

0.50

The height of the probability density function f(x) of the uniform distribution defined on the interval [a,b] is

1b−a between a and b, and zero otherwise.

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)

Due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to

P(Z < -1.5)

P(Z<0) equals ____. Select all that apply.

P(Z>0) 0.5 P(Z≤0)

The z table in the text provides the cumulative probability for a given value z. What does "cumulative probability" mean?

P(Z≤z)

The exponential distribution is related to which distribution?

The Poisson distribution

Which of the following are true about the normal curve? Select all that apply.

The area above the mean equals the area below the mean. The total area under the curve equals 1.

Which one of the following is true?

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

Which of the following is true about the formula for finding the 83rd percentile? Select all that apply.

The z-value would be positive. The percentile would be greater than the mean.

True or false: Statistical inference is generally based on the assumption of the normal distribution.

True

Transforming normal random variables

allows for the z-table to be used for determining probabilities.

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

equal to 0.5

The Poisson random variable counts the number of occurrences of an event over a given interval of time or space while the ______ distribution describes the time that elapses between such occurrences.

exponential

For a continuous random variable, one characteristic of its probability density function f(x) is that

f(x) ≥ 0 for all values x of X.

For a continuous random variable X it is only meaningful to calculate the probability that the value of the random variable

falls within some specified interval.

Which of the following BEST describes the shape of the normal distribution?

unimodal and symmetric

Percentiles for a normally distributed random variable can be found most easily by using which of the following formulas?

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−μσ

If the P(Z<z) is less than 0.5, then

z must be negative.

If the P(Z>z) is less than 0.5, then

z must be positive.

The probability that a continuous random variable X assumes a particular value x is

zero.

What does it mean to say that the exponential distribution is "memoryless"?

It has a constant failure rate.

All of the following are characteristics of the normal distribution EXCEPT:

It is a discrete distribution.

What can be said about the expected value and standard deviation of an exponential distribution?

The expected value is equal to the standard deviation.

Why is the normal distribution such an important probability distribution?

The normal distribution plays a key role in statistical inference.

A continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The expected value of X is calculated as ______.

a+b2

The purpose of the standard transformation is to

allow for the calculation of probabilities of any normal random variable.

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

bell shaped

For a z-value greater than 0, the P(Z<z) will be

between 0.5 and 1.

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

compute x values for given probabilities

A continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x)

is constant for all x between a and b, and 0 otherwise.

A random variable X follows the continuous uniform distribution if

it has an equally likely chance of assuming any value within a specified range.

For a z-value less than 0, the P(Z<z) will be

less than 0.5.

A continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The ______ of X is calculated using the formula (b−a)212‾‾‾‾‾‾√.

standard deviation

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

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

Since the z table provides the cumulative probabilities for a given value of z, what is the P(0 < Z < z)?

the result of subtracting 0.5 from the value found by looking up z in the table.

Since the z table provides the cumulative probabilities for a given value of z, what is the P(Z < z)?

the value found by looking up z in the table.

The exponential random variable is bounded below by _______.

zero

The exponential distribution is ______.

not symmetric

The exponential distribution is based entirely on

one parameter.

A noted feature of the exponential distribution is that it is blank , Incorrect Unavailable, thus implying a constant failure rate.

memoryless