Deck 5: Discrete Probability Distributions

Question 1

The only two types of random variables are discrete and continuous random variables.

Answer 1

True

Question 2

When a single value is randomly chosen from a discrete distribution, the different possible values are mutually exclusive.

Answer 2

True

Question 3

If a random variable is discrete, it means that the outcome for the random variable can take on only one of two possible values.

Answer 3

False

Question 4

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information, the expected number of injuries per weekend is 2.25.

Question 5

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the profit standard deviation for the company if it takes the contract is < $20,000.

Question 6

A random variable is generated when a variable's value is determined by using classical probability.

Question 7

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being at least $80,000 is 0.85.

Question 8

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the expected profit for the company if it takes the contract is $67,000.

Question 9

A probability distribution with an expected value greater than the expected value of a second probability distribution will also have a higher standard deviation.

Question 10

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

Question 11

The time required to assemble two components into a finished part is recorded for each employee at the plant. The resulting random variable is an example of a continuous random variable.

Question 12

The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information, the most likely number of no-shows on any given day is 0 customers.

Question 13

The Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week. Then the variable, number of showings, is a continuous distribution.

Question 14

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being < $80,000 is 0.55.

Question 15

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability that the profit is $80,000 or less is 0.55.

Question 16

When a market research manager records the number of potential customers who were surveyed indicating that they like the product design, the random variable, number who like the design, is a discrete random variable.

Question 17

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

Question 18

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information, the standard deviation for the number of no-shows is about 0.36 customers.

Question 19

The random variable, number of customers entering a store between 9 AM and noon, is an example of a discrete random variable.

Question 20

The number of no-shows each day for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information, the expected number of no-shows is 1.65 customers.

Question 21

The Ace Construction Company has entered into a contract to widen a street in Boston. The possible payoffs for this project have been determined by management. The probabilities for these payoffs could be determined using a binomial distribution.

Question 22

A direct marketing company believes that the probability of making a sale when a call is made to an individual's home is .02. The probability of making 2 or 3 sales in a sample of 20 calls is .0593.

Question 23

Each week American Stores receives a shipment from a supplier. The contract specifies that the maximum allowable percent defective is 5 percent. When the shipment arrives, a sample of 20 parts is randomly selected. If 2 or more of the sampled parts are defective, the shipment is rejected and returned to the supplier. Assume that a shipment arrives that actually has 4 percent defective parts and the distribution of defective parts is described by a binomial distribution. The probability that the shipment is rejected is approximately 0.19.

Question 24

Ace Computer Manufacturer buys disk drives in lots of 5,000 units from a supplier in California. The contract calls for, at most, 3 percent of the disk drives to be defective. When a shipment arrives, a sample of n = 15 parts is selected. If zero defects are found in this sample, the shipment is accepted. If 3 or more defects are found, the shipment is rejected and sent back to the supplier. If the number of defects found is 1 or 2, a second sample of 15 parts is selected. If this sample yields 1 or fewer defects, the shipment is accepted; otherwise the shipment is rejected. Based on a binomial distribution, the probability that Ace will reject a shipment of parts that meets the contract requirements is approximately 0.0355.

Question 25

In a Florida town, the probability distribution for the number of legitimate emergency calls per day for the Fire Department is given as follows. Also shown is the probability distribution for the number of false alarms: Given this information, the expected number of total calls to the fire department is 1.60 calls.

Question 26

The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the probability that more than 20 customers in the sample will request nonsmoking rooms is approximately 0.09.

Question 27

Each week American Stores receives a shipment from a supplier. The contract specifies that the maximum allowable percent defective is 5 percent. When the shipment arrives, a sample of 20 parts is randomly selected. If 2 or more of the sampled parts are defective, the shipment is rejected and returned to the supplier. Assume that a shipment arrives that actually has 4 percent defective parts and the distribution of defective parts is described by a binomial distribution. The probability that the shipment is accepted is approximately 0.81

Question 28

A pizza restaurant uses 7 different toppings on its pizzas. At lunch time it has a pizza buffet and makes pizzas with 2 toppings. If it wants to serve every possible combination of 2 toppings, it would need to make 14 different pizzas.

Question 29

Holmstead Company owns two small engine repair stores. The expected value of the number of complaints received per month at store 1 is 4.5 complaints. Further, the expected number of complaints per month for store 1 and store 2 combined is 13.6. This means the expected number of complaints per month at store 2 must be 9.1 complaints.

Question 30

The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the probability that fewer than 5 customers will request smoking rooms is approximately 0.09.

Question 31

A construction company has found it has a probability of 0.10 of winning each time it bids on a project. The probability of winning a given number of projects out of 12 bids could be determined with a binomial distribution.

Question 32

The number of defects discovered in a random sample of 100 products produced at the Berdan Manufacturing Company is binomially distributed with p = .03. Based on this, the standard deviation of the number of defects per sample of size 100 is 2.91.

Question 33

The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the expected number of requests for nonsmoking rooms is 14.

Question 34

When using the binomial distribution, the maximum possible number of success is the number of trials.

Question 35

The distribution for the number of emergency calls to a city's 911 emergency number in a one-hour time period is likely to be described by a binomial distribution.

Question 36

One difference between the binomial distribution and Poisson distribution is that the binomial's upper bound is the number of trials while the Poisson has no particular upper bound.

Question 37

Bill Price is a sales rep in northern California representing a line of athletic socks. Each day, he makes 10 sales calls. The chance of making a sale on each call is thought to be 0.30. The probability that he will make exactly two sales is approximately 0.2335.

Question 38

One of the characteristics of the binomial distribution is that the probability of success for each trial depends on whether the previous trial was a success or not.

Question 39

The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms. Recently, the customer service manager for the company randomly selected 25 calls. Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution, the standard deviation of requests for nonsmoking rooms is 5.25 customers.

Question 40

Six managers at a company all enjoy golf. Each Saturday, four of the six get together for 18 holes of golf. They have decided to set up a schedule so that the same foursome does not play twice before all possible foursomes have played. The number of weekends that will pass before the same group would play twice is 15.

Question 41

A warehouse contains 5 parts made by the Stafford Company and 8 parts made by the Wilson Company. If an employee selects 3 of the parts from the warehouse at random, the probability that all 3 parts are from the Wilson Company is approximately .1958.

Question 42

The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that exactly 8 customers will arrive in a one-hour period is 0.1366.

Question 43

The primary difference between the binomial distribution and the Poisson distribution is that the Poisson is used to describe a continuous random variable and the binomial is used for discrete random variables.

Question 44

The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m. is described by a Poisson distribution with mean equal to 15. Given this information, the expected number of calls in the first 30 minutes is 7.5 calls.

Question 45

The Brockingham Carpet Company prides itself on high quality carpets. At the end of each day, the company quality managers select 3 square yards for inspection. The quality standard requires an average of no more than 2.3 defects per square yard. The expected number of defects that the inspector will find during the inspection is 6.9.

Question 46

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will end up being 100 percent inspected is approximately .0746.

Question 47

The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that between 2 and 3 customers inclusively will arrive in one hour is 0.0263.

Question 48

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that contains twice the amount of defects allowed by the contract requirements will be shipped without further inspection is approximately .3874.

Question 49

The probability of the outcome changes from trial to trial in a binomial experiment.

Question 50

The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. The probability that more than 4 customers will arrive in a 30-minute period is 0.1933.

Question 51

A company has 20 copy machines and every day there is a 5 percent chance for each machine that it will not be working that day. If the company wants to calculate the probability of, say, 2 machines not working, it should use the Poisson distribution.

Question 52

A warehouse contains 5 parts made by the Stafford Company and 8 parts made by the Wilson Company. If an employee selects 3 of the parts from the warehouse at random, the probability that none of the 3 parts is from the Wilson Company is approximately .03496.

Question 53

A company has 20 cars that are available for use by company executives for official business purposes. Six of these cars are SUVs, 8 are luxury type cars, and the rest are basic sedans. Suppose the cars are randomly assigned each week. If 5 cars are put into use, the chance that none of the SUVs or luxury cars will be in the group is approximately .0004.

Question 54

The makers of Crustfree Bread in Boston have a quality standard that allows no more than 3 burned loaves per batch on average. Recently, the manager inspected a batch and found 5 burned loaves. She did not appear to be upset at the production meeting. This is because the chance of exactly 5 burned loaves occurring is 0.1008.

Question 55

The city council consists of 3 Democrats, 5 Republicans and 3 independents. Subcommittees are supposed to be randomly assigned from the council. Suppose the 5-member planning and zoning subcommittee is composed of 3 Democrats and 2 Republicans. The probability of this happening by chance alone is approximately .4545.

Question 56

The primary application for the hypergeometric probability distribution is in situations where the sampling is done without replacement from a finite population.

Question 57

The makers of Crustfree Bread in Boston have a quality standard that allows for no more than 3 burned loaves per batch on average. Assuming that the average of 3 per batch is being met, the standard deviation for the number of burned loaves in 4 batches is approximately 1.73 loaves.

Question 58

The Brockingham Carpet Company prides itself on high quality carpets. At the end of each day, the company quality managers select 3 square yards for inspection. The quality standard requires an average of no more than 2.3 defects per square yard. Last night, the inspector found 8 defects in the sample of 3 square yards. The chance of finding 8 or more defects in the sample is 0.9975.

Question 59

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will be shipped without further inspection is approximately .9139.

Question 60

The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m. is described by a Poisson distribution with mean equal to 15. Given this information, the standard deviation for the call distribution is about 3.87 calls.

Question 61

Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands can't be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. If people really can't tell the difference, the expected number of correct identifications in the sample would be:

A) 10.
B) 0.
C) between 4 and 9.
D) Can't be determined without more information.

Question 62

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Based on this distribution, the expected number of accidents in a given day is:

A) 0.30
B) 1.65
C) 2.00
D) 2.50

Question 63

Which of the following statements is incorrect?

A) The expected value of a discrete probability distribution is the long-run average value assuming the experiment will be repeated many times.
B) The standard deviation of a discrete probability distribution measures the average deviation of the random variable from the mean.
C) The distribution is considered uniform if all the probabilities are equal.
D) The mean of the probability distribution is equal to the square root of the variance.

Question 64

Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands can't be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. Suppose 14 people correctly identified the soft drink brand. Which of the following conclusions would be warranted under the circumstance?

A) Since the chance of getting 14 correct is 0.0370, which is quite small, the study shows that people are not able to identify brands effectively.
B) Since the probability of getting 14 or more correct is 0.0577, which is quite low, this means that people are not effective in identifying the soft drink brand.
C) Since the probability of getting 14 or more correct is 0.0577, which is quite low, the conclusion could be that people are effective at identifying soft drink brands.
D) The expected value for this binomial distribution is very close to 14 so this supports that people cannot tell the difference.

Question 65

A package delivery service claims that no more than 5 percent of all packages arrive at the address late. Assuming that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected and the 5 percent rate holds, what is the probability that more than 2 packages will be delivered late?

A) 0.0115
B) 0.0105
C) 0.0862
D) 0.0746

Question 66

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: This distribution is an example of:

A) a uniform distribution.
B) a continuous probability distribution.
C) a discrete probability distribution.
D) an expected value distribution.

Question 67

The Vardon Exploration Company is getting ready to leave for South America to explore for oil. One piece of equipment requires 10 batteries that must operate for more than 2 hours. The batteries being used have a 15 percent chance of failing within 2 hours. The exploration leader plans to take 15 batteries. Assuming that the conditions of the binomial apply, the probability that the supply of batteries will contain enough good ones to operate the equipment is:

A) 0.0449
B) 0.9832
C) 0.0132
D) 0.9964

Question 68

Many people believe that they can tell the difference between Coke and Pepsi. Other people say that the two brands can't be distinguished. To test this, a random sample of 20 adults was selected to participate in a test. After being blindfolded, each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was. If people really can't tell the difference, the probability that fewer than 6 people will guess correctly is:

A) 0.0148
B) approximately 0.02
C) 0.0307
D) 0.0514

Question 69

A package delivery service claims that no more than 5 percent of all packages arrive at the address late. Assuming that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected, and the 5 percent rate holds, what is the probability that exactly 2 packages in the sample arrive late?

A) 0.0746
B) 0.9884
C) 0.2347
D) 0.0439

Question 70

A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day: The expected number of successful sales calls per day is:

A) 2.00
B) 1.15
C) 1.90
D) 2.50

Question 71

The Vardon Exploration Company is getting ready to leave for South America to explore for oil. One piece of equipment requires 10 batteries that must operate for more than 2 hours. The batteries being used have a 15 percent chance of failing within 2 hours. The exploration leader plans to take 15 batteries. Assuming that the conditions of the binomial apply, the probability that the supply of batteries will not contain enough good ones to operate the equipment is:

A) 0.0449
B) 0.0132
C) 0.9832
D) 0.0168

Question 72

Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi. Recently, an independent research firm questioned a random sample of 25 adult non-diet cola drinkers. That chance that 20 or more of these people will prefer Coca-Cola is:

A) essentially zero.
B) 0.0199.
C) 0.0294.
D) None of the above

Question 73

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is hypergeometric.

Question 74

The probability function for random variable X is specified as: The expected value of X is

A) 0.333
B) 0.500
C) 2.000
D) 2.333

Question 75

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: The probability of having less than 2 accidents on a given day is:

A) 0.30
B) 0.75
C) 0.45
D) 0.25

Question 76

A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day: Based on this information, the probability that the sales rep will have a total of 2 successful calls in a two- day period is:

A) 0.60
B) 0.09
C) 0.15
D) 0.06

Question 77

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Based on this probability distribution, the standard deviation in the number of accidents per day is:

A) 2.0
B) 1.63
C) 2.65
D) 1.28

Question 78

A sales rep for a national clothing company makes 4 calls per day. Based on historical records, the following probability distribution describes the number of successful calls each day: Based on the information provided, what is the probability of having at least 2 successful calls in one day?

A) 0.60
B) 0.20
C) 0.30
D) 0.10

Question 79

Consider the following two probability distributions: Which of the following is an accurate statement regarding these two distributions?

A) Distribution A has a higher variance.
B) Distribution B has a higher variance.
C) Both distributions are positively skewed.
D) Both distributions are uniform.

Question 80

Which of the following is not a condition of the binomial distribution?

A) Two possible outcomes for each trial
B) The trials are independent.
C) The standard deviation is equal to the square root of the mean.
D) The probability of a success remains constant from trial to trial.