Stats-Exam 2

The uniform probability distribution is used with a. a continuous random variable b. a discrete random variable c. a normally distributed random variable d. any random variable, as long as it is not nominal

a. a continuous random variable

The weight of an object is an example of a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the weight of the object d. either a continuous or a discrete random variable depending on the units of measurement

a. a continuous random variable

For the standard normal probability distribution, the area to the left of the mean is a. -0.5 b. 0.5 c. any value between 0 to 1 d. 1

0.5

The number of customers that enter a store during one day is an example of a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the number of the customers d. either a continuous or a discrete random variable, depending on the gender of the customers

b. a discrete random variable

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials? a. 0.0036 b. 0.0600 c. 0.0555 d. 0.2800

c. 0.0555

The binomial probability distribution is used with a. a continuous random variable b. a discrete random variable c. any distribution, as long as it is not normal d. None of these alternatives is correct.

b. a discrete random variable

Which of the following is not a property of a binomial experiment? a. the experiment consists of a sequence of n identical trials b. each outcome can be referred to as a success or a failure c. the probabilities of the two outcomes can change from one trial to the next d. the trials are independent

c. the probabilities of the two outcomes can change from one trial to the next

For a normal distribution, a negative value of z indicates a. a mistake has been made in computations, because z is always positive b. the area corresponding to the z is negative c. the z is to the left of the mean d. the z is to the right of the mean

c. the z is to the left of the mean

A random variable that may take on any value in an interval or collection of intervals is known as a a. continuous random variable b. discrete random variable c. continuous probability function d. finite probability function

a. continuous random variable

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a a. discrete random variable b. continuous random variable c. complex random variable d. simplex random variable

a. discrete random variable

A simple random sample from an infinite population is a sample selected such that a. each element is selected independently and from the same population b. each element has a 0.5 probability of being selected c. each element has a probability of at least 0.5 of being selected d. the probability of being selected changes

a. each element is selected independently and from the same population

A normal probability distribution a. is a continuous probability distribution b. is a discrete probability distribution c. can be either continuous or discrete d. must have a standard deviation of 1

a. is a continuous probability distribution

The mean of a standard normal probability distribution a. is always equal to zero b. can be any value as long as it is positive c. can be any value d. is always greater than zero

a. is always equal to zero

A description of the distribution of the values of a random variable and their associated probabilities is called a a. probability distribution b. random variance c. random variable d. expected value

a. probability distribution

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have a. the same probability of being selected b. a probability of 1/n of being selected c. a probability of 1/N of being selected d. a probability of N/n of being selected

a. the same probability of being selected

The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

a. yes f(x) 0 and f(x) = 1

Variance is a. a measure of the average, or central value of a random variable b. a measure of the dispersion of a random variable c. the square root of the standard deviation d. the sum of the squared deviation of data elements from the mean

b. a measure of the dispersion of a random variable

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a a. discrete random variable b. continuous random variable c. complex random variable d. simplex random variable

b. continuous random variable

Doubling the size of the sample will a. reduce the standard error of the mean to one-half its current value b. reduce the standard error of the mean to approximately 70% of its current value c. have no effect on the standard error of the mean d. double the standard error of the mean

b. reduce the standard error of the mean to approximately 70% of its current value

For a uniform probability density function, a. the height of the function cannot be larger than one b. the height of the function is the same for each value of x c. the height of the function is different for various values of x d. the height of the function decreases as x increases

b. the height of the function is the same for each value of x

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is a. different for each interval b. the same for each interval c. at least one d. None of these alternatives is correct.

b. the same for each interval

Which of the following is not a characteristic of the normal probability distribution? a. symmetry b. The total area under the curve is always equal to 1. c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean d. The mean is equal to the median, which is also equal to the mode.

c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

The expected value for a binomial probability distribution is a. E(x) = Pn(1 - n) b. E(x) = P(1 - P) c. E(x) = nP d. E(x) = nP(1 - P)

c. E(x) = nP

Which of the following statements about a discrete random variable and its probability distribution are true? a. Values of the random variable can never be negative. b. Some negative values of f(x) are allowed as long as f(x) = 1. c. Values of f(x) must be greater than or equal to zero. d. The values of f(x) increase to a maximum point and then decrease.

c. Values of f(x) must be greater than or equal to zero.

If we consider the simple random sampling process as an experiment, the sample mean is a. always zero b. always smaller than the population mean c. a random variable d. exactly equal to the population mean

c. a random variable

A random variable that can assume only a finite number of values is referred to as a(n) a. infinite sequence b. finite sequence c. discrete random variable d. discrete probability function

c. discrete random variable

A measure of the average value of a random variable is called a(n) a. variance b. standard deviation c. expected value d. coefficient of variation

c. expected value

Which of the following is not a required condition for a discrete probability function? a. f(x) 0 for all values of x b. f(x) = 1 for all values of x c. f(x) = 0 for all values of x d. f(x) 1 for all values of x

c. f(x) = 0 for all values of x

In computing the standard error of the mean, the finite population correction factor is used when a. N/n > 0.05 b. N/n 0.05 c. n/N > 0.05 d. n/N 30

c. n/N > 0.05

A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately a. normal because is always approximately normally distributed b. normal because the sample size is small in comparison to the population size c. normal because of the central limit theorem d. None of these alternatives is correct.

c. normal because of the central limit theorem

The standard deviation of a point estimator is called the a. standard deviation b. standard error c. point estimator d. variance of estimation

c. point estimator

As the sample size increases, the a. standard deviation of the population decreases b. population mean increases c. standard error of the mean decreases d. standard error of the mean increases

c. standard error of the mean decreases

A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is a. zero b. (a - b) c. (b - a) d. 1/(b - a)

d. 1/(b - a)

X is a random variable with the probability function: f(X) = X/6 for X = 1, 2 or 3 The expected value of X is a. 0.333 b. 0.500 c. 2.000 d. 2.333

d. 2.333

The expected value of a discrete random variable a. is the most likely or highest probability value for the random variable b. will always be one of the values x can take on, although it may not be the highest probability value for the random variable c. is the average value for the random variable over many repeats of the experiment d. None of these alternatives is correct.

d. None of these alternatives is correct.

The expected value of a random variable is a. the value of the random variable that should be observed on the next repeat of the experiment b. the value of the random variable that occurs most frequently c. the square root of the variance d. None of these alternatives is correct.

d. None of these alternatives is correct.

Which of the following is not a characteristic of the normal probability distribution? a. The mean, median, and the mode are equal b. The mean of the distribution can be negative, zero, or positive c. The distribution is symmetrical d. The standard deviation must be 1

d. The standard deviation must be 1

Which of the following is a required condition for a discrete probability function? a. f(x) = 0 for all values of x b. f(x) 1 for all values of x c. f(x) < 0 for all values of x d. f(x) = 1 for all values of x

d. f(x) = 1 for all values of x

The standard deviation is the a. variance squared b. square root of the sum of the deviations from the mean c. same as the expected value d. positive square root of the variance

d. positive square root of the variance

A numerical description of the outcome of an experiment is called a a. descriptive statistic b. probability function c. variance d. random variable

d. random variable