Chapter 6 LearnSmart

Due to symmetry, the probability that the standard normal random variable Z is less than 0 is equal to A. 0.5 B. 0.75 C. 0 D. 1.0

A. 0.5

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

C. P(X<20) is greater than P(X<16)

due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to A. P(Z>1)+P(Z>0.5) B. P(Z<1.5) C. P(Z<-1.5) D. P(Z>-1.5)

C. P(Z<-1.5)

The probability that the normal random variable Z is less than 1.5 is equal to A. P(z>1)+P(Z>0.5) B. P(Z<-1.5) C. P(Z>-1.5) D. P(Z>1.5)

C. P(Z>-1.5)

The probability distribution of a discrete random variable is called its probability ___________. A. expected value function B. density function C. variance function D. mass function

D. mass function

The inverse transformation, x=µ+ zsigma is used to ___________ A. calculate probabilities using known x values B. compute x values for given probabilities C. calculate z values using known x values

B. compute x values for given probabilities

The total area under the normal curve is _________. A. between -1 and 1 B. equal to 1 C. less than 1 D. greater than 1

B. equal to 1

If X is a normally distributed random variable then, A. the mean is less than the median which is less than the mode B. the mean, the median, and the mode are all equal C. the mean is greater than the median which is greater than the mode D. there is no particular relationship between the mean, the median, and mode

B. the mean, the median, and the mode are all equal

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. b-a/2 B. 1/b-a C. √(b-a^2/12 D. a+b/2

D. a+b/2

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

D. continuous uniform distribution

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

A. there are a countable number of possible values

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

D. continuous uniform distribution

For a continuous random variable X, the cumulative distribution function F(x) provides the probability that X is A. not equal to a particular value x B. equal to any value x C. greater than any value x D. less than or equal to any value x

D. less than or equal to any value x

All of the following are characteristics of the normal distribution EXCEPT: A. it is a discrete distribution B. it is symmetric around its mean C. It is asymptotic D. It is completely described by two parameters

A. it is a discrete distribution

The normal distribution is completely described by these two parameters: A. mean and variance B. median and mean C. mean and range D. median and range

A. mean and variance

The probability of distribution of a continuous random variable is called its A. probability density function B. probability mass function C. probability modal function

A. probability density function

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

D. equal to one

For a continuous random variable X, how many distinct values can it assume over an interval? A. finite B. countably infinite C. countably finite D. infinite

D. infinite

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

A. P(X>16) is greater than P(X<16)

For a continuous random variable X, the function used to find the area under f(x) up to any value x is called the A. cumulative distribution function B. poisson mass function C. binomial mass function D. normal mass function

A. cumulative distribution function

(refer to question 34 photo) The accompanying table shows a portion of the z table. Find the probability that Z is greater than -2.22. A. 0.9868 B. 0.0132 C. 0.0139 D. 0.9778

A. 0.9868

(refer to question 19 photo) The accompanying table shows a portion of the z table. Find the z value that satisfies P(Z<or equal to z) = 0.9207 A. 1.41 B. -1.40 C. 1.40 D. -1.41

A. 1.41

Since the z table provides the cumulative probabilities for a given value of z, how can we calculate P(Z>z)? A. =1-P(Z<or equal to z) B. =P(Z<or equal to z)-0.5 C. =0.5-P(Z<or equal to z) D. =P(Z< or equal to z)

A. =1-P(Z<or equal to z)

For data that are normally distributed, the percentage of the data that falls within two standard deviations of the mean is A. 32% B. 68% C. 5% D. 95%

B. 68%

For data that a normally distributed, the percentage of the data that falls within two standard deviations of the mean is A. 32% B. 95% C. 5% D. 68%

B. 95%

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

B. the probability that Z is less than or equal to a given z value

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

B. the probability that Z is less than or equal to a given z value

Which of the following BEST describes the shape of the normal distribution? A. negatively skewed B. unimodal and symmetric C. positively skewed D. unimodal and skewed

B. unimodal and symmetric

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

C. 10% From the empirical rule, 68% of the return fall between 2% and 22%, thus 32% of returns are greater than 22% or less than 2%. From symmetry, half of 32% or 16% will be less than 2%

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

C. P(X<20) is greater than P(X<16)

The shape of the graph depicting the normal probability density function is __________. A. negatively skewed B. a straight line C. bell shaped D. positively skewed

C. bell shaped

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

C. between zero and one

The mean of the standard normal distribution is equal to ________. A. two B. one-half C. zero D. one

C. zero

The mean and variance of the standard normal distribution are _______, respectively. A. 0 and 0 B. 1 and 0 C. 1 and 1 D. 0 and 1

D. 0 and 1

An investment strategy has an expected return of 12 percent and a standard deviation of 10 percent. If investment returns are normally distributed, the probability of earning a return of more than 32 percent is CLOSEST to: A. 5% B. 95% C. 16% D. 2.5%

D. 2.5%

Which of the following statements is MOST accurate? A. For data the are normally distributed, 68% of the data will fall within 2 standard deviations of the mean B. For the data that are normally distributed, 32% of the data will fall within 2 standard deviations of the mean C. For the data that are normally distributed, 5% of the data will fall into 2 standard deviations D. For data that are normally distributed, 95% of the data will fall within 2 standard deviations of the mean

D. For data that are normally distributed, 95% of the data will fall within 2 standard deviations of the mean

Which of the following can be represented by a discrete random variable? A. the circumference of a randomly generated circle B. the average distance achieved in a series of long jumps C. the flight time of an airline flight between Chicago and New York D. The number of defective light bulbs in a sample of 5

D. The number of defective light bulbs in a sample of 5

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

D. the number of states in the USA

Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula: A. x= z-µ/sigma B. x=z-sigma/µ C. x=z+µsigma D. x=µ+zsigma

D. x=µ+zsigma

A normal random variable X is transformed into Z by __________ A. adding the standard deviation, and then dividing the mean B. multiplying by the standard deviation, and then subtracting the mean C. adding the mean and then multiplying by the standard deviation D.subtracting the mean, and then dividing by the standard deviation

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

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

False --A continuous random variable assumes an infinite number of values over an interval