BUS 281: Chapter 6 - Continuous Probability Distributions

The inverse transformation, x = μ + zσ is used to ___________________. -compute x values for given probabilities -calculate probabilities using known x values -calculate z values using known x values

-compute x values for given probabilities

Which of the following random variables is depicted with a bell-shaped curve? -A binomial random variable -A uniform random variable -A normal random variable -An exponential random variable

-A normal random variable

True or false: The distinct values of both a continuous random variable and a discrete random variable can be counted.

-False

True or false: The expected value and the variance of the standard normal random variable Z are both zero.

-False

The probability that a discrete random variable X assumes a particular value x is ______________. -between -1 and 1 -between zero and one -between zero and infinity -always zero

-between zero and one

For a discrete random variable X, ___________________. -it is not possible to compute the probability that it assumes a particular value x -there is a probability density function that describes it -there are a countable number of possible values -there are an infinite number of values within an interval

-there are a countable number of possible values

Which of the following BEST describes the shape of the normal distribution? -negatively skewed -unimodal and systematic -positively skewed -unimodal and skewed

-unimodal and systematic

Due to symmetry, the probability that the normal random variable Z is greater than 0 is ___________. -greater than 1.0 -between 0 and 1 -equal to 0.5 -equal to 1.0

-equal to 0.5

For a continuous random variable, one characteristic of its probability density function f(x) is that the area under f(x) over all values of x is __________. -less than zero -equal to one -greater than one -equal to zero

-equal to one

A characteristic of the normal distribution is that ____________. -it is asymptotic -it crosses the horizontal axis -it is completely described by four parameters -its mean is not equal to its medium

-it is asymptotic

The probability distribution of a discrete random variable is called its probability _________________ -expected value function -variance function -density function -mass function

-mass function

The normal distribution is completely described by these two parameters: -mean and range -median and mean -median and range -mean and variance

-mean and variance

A normal random variable X is transformed into Z by ________________. -subtracting the mean, and then dividing by the standard deviation -adding the standard deviation, and then dividing by the mean -adding the mean and then multiplying by the standard deviation -multiplying by the standard deviation, and then subtracting the mean

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

All of the following are examples of random variables that are likely follow a normal distribution EXCEPT _______________. -the scores on the SAT -the debt of college graduates -the weights of newborn babies -the number of states in the USA

-the number of states in the USA

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

-continuous uniform distribution

Suppose you were told that the delivery time of your new washing machine is equally likely over the time period 9 am to noon. If we define the random variable X as delivery time, then X follows the _________________. -binomial distribution -continuous uniform distribution -discrete uniform distribution -normal distribution

-continuous uniform distribution

For a continuous random variable X, the function used to find the area under f(x) up to any value x is called the _____________. -binomial mass function -normal mass function -cumulative distribution function -Poisson mass function

-cumulative distribution function

How many parameters are needed to fully describe any normal distribution? a) 2 b) 1 c) 4 d) 3

a) 2

The area under a normal curve below its expected value is _______. a) 0 b) 1.0 c) 0.75 d) 0.50

d) 0.50

The z table provides the cumulative probabilities for a given z. What does "cumulative probabilities" mean? -The probability that Z is equal to a given z value -The probability that Z is less than or equal to a given z value -The probability that Z is greater than or equal to a given Z value -The probability of the sum of two values of Z

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

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the P(X<20) related to the P(X<16)? -No comparison can be made with the given information -P(X<20) is greater than P(X<16) -P(X<20) is less than P(X<16) -P(X<20) is equal to P(X<16)

-P(X<20) is greater than P(X<16)

True or false: A discrete random variable can assume an uncountable number of values

-False

An investment strategy has an expected return of 12 percent and a standard deviation of 10 percent. If an investment returns are normally distributed, the probability of earning a return less than 2 percent is CLOSEST to: a) 68% b) 16% c) 32% d) 10

b) 16%

For data that are normally distributed, the percentage of the data that falls within one standard deviations of the mean is ___________. a) 5% b) 68% c) 95% d) 32%

b) 68%

For data that are normally distributed, the percentage of the data that falls within two standard deviations of the mean is ___________. a) 5% b) 68% c) 95% d) 32%

c) 95%

If X is normally distributed random variable, then ________________. -there is no particular relationship between the mean, median, and mode -the mean, median, and mode are all equal -the mean is less than the median which is less than the mode -the mean is greater than the median which is greater than the mode

the mean, median, and mode are all equal