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2. A random variable can be defined as: Multiple choice question. One from a set of variables representing different outcomes to a chance experiment Reason: One variable is used to represent all outcomes. a variable chosen by chance to represent the outcomes of an experiment Reason: It is the value, not the variable that is random. a quantity resulting from a random experiment that can have different values Choose the random variables from this set that are discrete. Select all that apply. Multiple select question. Number of drive-thru customers to the bank on a given day. The number of dots uppermost of rolling a pair of dice. The weight of a bag of a dozen apples. Reason: The bag can take on any weight over a given range, say 9 to 10 pounds. The travel time of an airline flight. Reason: The travel time can take on any value over a given range, say 1 to 2 hours. What shows the possible outcomes of a random experiment and the probability of each outcome? Multiple choice question. A Scatter Diagram Reason: A scatter diagram shows the relationship between two variables. See Chapter 4. A Random Number Table Reason: A random number table is just a listing of the digits 0-9 listed in random order. A Stem and Leaf Plot Reason:

This is a descriptive tool for displaying data. See Chapter 4. A Probability Distribution Choose the two random variables from this list that are continuous. Multiple select question. The average temperature in NYC during May. The number of apples per bag in a supermarket. Reason: This random variable can assume only certain clearly separated values. The number of ads during a television show. Reason: This random variable can assume only certain clearly separated values. The wait time at the dentist. Choose the statements that describe characteristics of a Probability Distribution. Select all that apply. Multiple select question. The probability of an outcome is between 0 and 1 inclusive. The sum of the probabilities of all possible outcome is one. The distribution is symmetrical. Reason: Not necessarily. Half of the possible outcomes have associated probabilities greater than 0.5 Reason: All of the probabilities could be less than 0.5. The outcomes are mutually exclusive events. • Experiment matches Choice, selecting and weighing the apples selecting and weighing the apples • outcome matches Choice, 165 grams average weight 165 grams average weight • event matches Choice, an average weight between 150 and 165 grams an average weight between 150 and 165 grams • random variable matches Choice, The average weight of five apples The average weight of five apples

A quantity representing the outcome of a random experiment that can assume different values is called a: Multiple choice question. probability Reason: A probability is associated with a particular value of a random variable. mutually exclusive event Reason: The outcomes of a random variable that make up a probability distribution are mutually exclusive. random variable probability distribution Reason: A probability distribution describes a random variable. Choose the random variables from this set that are discrete. Select all that apply. Multiple select question. The number of persons riding on a bus. The life span of a parakeet. Reason: Life span is measurement of time, which is continuous. The number of concert tickets sold. The height of a person from a class of eight. Reason: Although the people are discrete, their height is not. Which of the following statements is the best definition of a Continuous Random Variable? Multiple choice question. A random variable that can assume any value within a range of values. A random variable that can assume only certain separate values. Reason: This is a discrete variable A random variable that has an infinite number of values, such as the whole numbers. Reason: A variable can take on an infinite number of values, but still be discrete, if there is a clear separation between values. In a binomial experiment the variable is the number of successes in a fixed number of trials and the probability of success is the same for each trial. Which two of the following statements also describe features of a binomial experiment? Multiple select question. Trials are independent. The distribution is always symmetrical. Reason:

It is only symmetrical if P(success)=50%. The trials represent selection without replacement. Reason: No. Independent trials imply replacement. The outcome of a trial can be classified as either a success or a failure. A random variable can be defined as: Multiple choice question. a quantity resulting from a random experiment that can have different values One from a set of variables representing different outcomes to a chance experiment Reason: One variable is used to represent all outcomes. a variable chosen by chance to represent the outcomes of an experiment Reason: It is the value, not the variable that is random. True or false: The standard deviation of a probability distribution is the square root of the variance of the probability distribution. True false question. True False Reason: The standard deviation is defined as the square root of the variance. Choose the two random variables from this list that are continuous. Multiple select question. The wait time at the dentist. The average temperature in NYC during May. The number of ads during a television show. Reason: This random variable can assume only certain clearly separated values.

The number of apples per bag in a supermarket. Reason: This random variable can assume only certain clearly separated values. The formula for the variance of a binomial distribution is σ 2 = nπ(1 - π). What do the symbols n and π represent in this formula? Multiple choice question. number of trials and P(success) number of trials and random variable Reason: number of trials and P(success) random variable and combination Reason: number of trials and P(success) combination and and P(success) Reason: number of trials and P(success) A Binomial experiment has independent trials and the outcome of a trial can be classified as either a success or a failure. Which two of the following statements also describe features of a binomial experiment? Multiple select question. After the first trial, subsequent trials are conditional probabilities. Reason: No. Independence implies that the trial probabilities are not changed by previous events. The random variable counts the number of successes in a fixed number of trials. The probability of success stays the same for each trial. The distribution is always asymmetric in shape. Reason: If P(success)=0.5 then the distribution is symmetrical. A binomial distribution has n = 10 trials with a probability of success of π=0.4. Calculate the mean of this binomial distribution,. Multiple choice question. 0.6 Reason: This is the probability of a failure. 0.4 Reason: This is the probability of a success. You must multiply this by the n. 4 5 Reason: Multiple n by π. 2.4

Reason: This is the variance. A binomial distribution has 8 trials and a probability of success of 0.2. Calculate the variance for this distribution. Multiple choice question. 1.60 Reason: This is the mean. 0.80 Reason: This is the probability of a failure. 1.28 1.13 Reason: This is the standard deviation. A software salesman knows that on average he will make one sale for every ten companies he calls. Let "success" be making a sale. (P(success)=0.10) Use binomial probability formula to find the chance that he will make two sales if he calls 6 companies. Multiple choice question. 0.250 Reason: x=2, n=6, π=0.1; P(2)= 6 C 2 (0.1) 2 (0.9) 4 0.033 Reason: x=2, n=6, π=0.1; P(2)= 6 C 2 (0.1) 2 (0.9) 4 0.333 Reason:

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