Statistics Chapter 6 Practice

True or false: The standard deviation of a probability distribution is the square root of the variance of the probability distribution. True False

True

A restaurant employs 16 people, 8 of whom are women. If five employees are chosen randomly to receive tickets to a concert, what is the probability (to two places accuracy) that three of them will be women? Use hyper-geometric distribution. a) 0.36 b) 0.56 c) 0.02 d) 0.15

a) 0.36

A binomial distribution has n=12 trials with a probability of success of pi=0.3. Calculate the mean of this binomial distribution. a) 3.6 b) 0.4 c) 6 d) 4

a) 3.6

What shows the possible outcomes of a random experiment and the probability of each outcome? a) A Probability Distribution b) A Random Number Table c) A Stem and Leaf Plot d) A Scatter Diagram

a) A Probability Distribution

Which of the following statements describes the relationship between the Poisson distribution and the binomial distribution?

a) It is a limiting form of the binomial distribution when the probability of success (pi) is very small and the sample (n) is very large.

Choose the two random variables from this list that are continuous. a) The average temperature in NYC during May. b) The compensation of a Top 500 CEO. c) The number of apples per bag in a supermarket. d) The number of ads during the Superbowl.

a) The average temperature in NYC during May. b) The compensation of a Top 500 CEO.

Which three of the following statements describe the Poisson Distribution? a) The intervals do not overlap and are independent. b) The probability of the event is proportional to the interval size. c) The probability of an individual event occurring is quite large. d) The random variable is the number of occurrences during an interval.

a) The intervals do not overlap and are independent. b) The probability of the event is proportional to the interval size. d) The random variable is the number of occurrences during an interval.

Select three of the following statements that describe a Probability Distribution. a) The list of possible outcomes is collectively exhaustive. b) The probability of some outcomes are greater than others. c) Any possible outcome has a probability between 0 and 1 inclusive. d) The distribution is "bell" shaped. e) The outcomes are mutually exclusive events.

a) The list of possible outcomes is collectively exhaustive. c) Any possible outcome has a probability between 0 and 1 inclusive. e) The outcomes are mutually exclusive events.

A Binomial experiment has independent trails, 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? a) The probability of success stays the same for each trial. b) The random variable counts the number of successes in a fixed number of trials. c) The distribution is always asymmetric in shape. d) After the first trial, subsequent trials are conditional possibilities.

a) The probability of success stays the same for each trial. b) The random variable counts the number of successes in a fixed number of trials.

A binomial experiment consists of tossing 10 coins and observing the number of "heads" that land up. Identify the two questions from this list that would usually be answered by using a cumulative probability distribution. a) What is the chance of four or fewer "heads"? b) What is the probability that all ten coins will be "heads"? c) What is the probability of exactly 6 "heads"? d) What is the probability of six or more "heads"?

a) What is the chance of four or fewer "heads"? d) What is the probability of six or more "heads"?

A bake shop sells twenty different kinds of pastry. Twelve of them are chocolate. In Nan randomly buys eight kinds a party, what are the chances that four of them will be chocolate? Use the hyper-geometric distribution. a) 0.52 b) 0.28 c) 0.09 d) 0.14

b) 0.28

A grocer checks 200 apples and finds that 8 are spoiled. On average, how many apples are spoiled in a bag of ten? (Hint: spoilage will follow a Poisson distribution, left n=10 and pi is the empirical probability.) a) 2 b) 0.4 c) 0.2 d) 0.04

b) 0.4

A binomial distribution has n=10 trials with a probability of success of pi=0.4. Calculate the mean of this binomial distribution. a) 0.4 b) 4 c) 0.8 d) 5

b) 4

Choose the three statements that describe characteristics of a Probability Distribution? a) The distribution is symmetrical. b) The probability of an outcome is between 0 and 1. c) The outcomes are mutually exclusive events. d) Half of the possible outcomes have associated probabilities greater than 0.5 e) The sum of the probabilities of all possible events is one.

b) The probability of an outcome is between 0 and 1. c) The outcomes are mutually exclusive events. e) The sum of the probabilities of all possible events is one.

From the following list, choose the two random variables that are continuous. a) The quantity of clubs in a poker hand b) The tire pressure in a randomly selected automobile c) The number of students attending a lecture d) The average annual return on a certain bond

b) The tire pressure in a randomly selected automobile d) The average annual return on a certain bond

It is easier to use a binomial probability table instead of calculating the probability under what circumstances? a) When n is small b) When n is large c) When pi is greater than one d) When pi is two or more digits

b) When n is large

A software salesman knows that on average he will make a sale for every ten companies he calls. Let "success" be making a sale. (I.e. P(success)=0.10) Use binomial probability formula to find the chance that he will make two sales if he calls 6 companies. a) 0.33 b) 0.250 c) 0.098 d) 0.033

c) 0.098

A bowl contains two white and four black marbles. A marble is randomly selected, its color noted, and returned to the bowl. Let "success" be selecting a white marble. (I.e. P(success)=2/6) Use the binomial probability formula to find the chance of selecting three white marbles in 8 draws. a) 0.422 b) 0.5 c) 0.273 d) 0.375

c) 0.273

A cellular communications company finds that on average it drops about 300 calls for every 1000 calls placed. What is the mean number of dropped calls for ten calls placed? (Hint: dropped calls follow a Poisson distribution. Let n=10 and pi is the empirical probability.) a) 3.33 b) 3% c) 3 d) 33%

c) 3

In a binomial experiment the trials are independent, and the probability of success is the same for each trial. Which two of the following statements also describe features of a binomial experiment? a) The distribution is always symmetrical. b) The trials represent selection without replacement. c) The outcome of a trial can be classified as either a success or a failure. d) The variable is the number of successes in a fixed number of trials.

c) The outcome of a trial can be classified as either a success or a failure. d) The variable is the number of successes in a fixed number of trials.

Under what circumstances should you use the hypergeometric distribution instead of the binomial distribution? Choose one. a) When the population size, N, is much larger than the sample size, n, meaning that the trials give approximately the same probability. b) When the observations are mutually exclusive and collectively exhaustive. c) When the sample size is more than 5% of the population so that the trials are not independent.

c) When the sample size is more than 5% of the population so that the trials are not independent.

A random variable can be defined as: a) a variable chosen by chance to represent the outcomes of an experiment. b) one from a set of variables representing different outcomes to a chance experiment c) a quantity resulting from a random experiment that can have different values.

c) a quantity resulting from a random experiment that can have different values.

A ____________ random variable can assume any value within a range of possible values.

continuous

A grocer finds that the average number of spoiled apples is 4% of the total. Use the Poisson distribution to find the probability that there will be one spoiled apple in a bag of ten apples. (Hint: calculate the Poisson mean) a) 0.94 b) 0.67 c) 0.38 d) 0.268

d) 0.268

A binomial distribution has 8 trials and a probability of success of 0.2. Calculate the variance for this distribution. a) 0.64 b) 1.6 c) 4 d) 1.28

d) 1.28

A _________________ random variable can assume only certain clearly separated values.

discrete