Question 1

The probability of receiving a 911 call on a university campus is the same every day.The probability of having received a 911 call on a single day does not change the probability of receiving a 911 call on any other day.Which of the following distributions would you use to determine the probability that a 911 call will be received next day?
A)Binomial distribution.
B)Poisson distribution.
C)Normal distribution.
D)Hypergeometric distribution.

Accepted Answer

The Poisson distribution is appropriate for modeling the number of rare events (in this case, the number of 911 calls) in a fixed interval of time or space, given that the events occur independently and with a constant rate. This distribution is characterized by a single parameter, λ, which represents the average rate of occurrence of the events. Therefore, to determine the probability that a 911 call will be received on the next day, we can use the Poisson distribution with the corresponding value of λ, which can be estimated from the historical data. The other distributions listed are not appropriate for this problem because they either require a fixed number of trials (Binomial), assume a normal population (Normal), or involve sampling without replacement (Hypergeometric), none of which apply here.

Question 2

The Tampa International Airport (TIA)has been criticized for the waiting times associated with departing flights.While the critics acknowledge that many flights have little or no waiting times, their complaints deal more specifically with the longer waits attributed to some flights.The critics are interested in showing, mathematically, exactly what the problems are.Which type of distribution would best model the waiting times of the departing flights at TIA?
A)Uniform distribution
B)Binomial distribution
C)Normal distribution
D)Exponential distribution

Accepted Answer

Exponential distribution is most appropriate for modeling waiting times, especially in contexts like airport departures where there can be a wide variation in wait times, with many short waits and a few much longer ones. This distribution is commonly used for such purposes because it can effectively represent the probability of waiting a certain amount of time until an event occurs.

Question 3

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women.Which of the following distributions would you use to determine the probability that half of the members will be women?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Binomial distribution.

Accepted Answer

The hypergeometric distribution is appropriate when sampling without replacement from a finite population. In this case, we are selecting 6 members from a pool of 18 men and 6 women, without replacement. The question asks for the probability that half of the members (3) will be women, which can be calculated using the hypergeometric distribution. The other distributions listed are not appropriate for this scenario.

Question 4

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 5 such alarms in your home and they operate independently.Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?
A)Binomial distribution.
B)Poisson distribution.
C)Normal distribution.
D)Hypergeometric distribution.

Accepted Answer

A binomial distribution is appropriate when there are a fixed number of independent trials, each with a binary outcome (success or failure), and a constant probability of success. In this scenario, we have 5 independent trials (the 5 smoke alarms), each with a binary outcome (the alarm either functions properly or it doesn't), and a constant probability of success (0.8).

Question 5

It was believed that the probability of being hit by lightning is the same during the course of a thunderstorm.Which of the following distributions would you use to determine the probability of being hit by a lightning during the first half of a thunderstorm?
A)Normal distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Exponential distribution.

Accepted Answer

The uniform distribution would be the best choice because it assumes that all outcomes within a given range are equally likely to occur. In this case, we are interested in the probability of being hit by lightning during the first half of a thunderstorm, which is a specific range of time during the storm. Therefore, the uniform distribution would be appropriate to model the probability of being hit during this time frame. The normal distribution assumes a bell-shaped curve, the Poisson distribution models the number of occurrences in a given time frame, and the exponential distribution models the time between occurrences, none of which would be appropriate for this scenario.

Question 6

A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).Which of the following distributions would you use to determine the probability that all of them will fail?
A)Binomial distribution.
B)Poisson distribution.
C)Normal distribution.
D)Hypergeometric distribution.

Accepted Answer

The binomial distribution can be used to model the number of successes in a fixed number of independent trials, where the probability of success is constant. In this case, we have three independent trials (three businesses opening) with a constant probability of success (0.4), and we are interested in the probability of all three trials resulting in failure.

Question 7

From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed.Which of the following distributions would you use to determine the probability that out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Binomial distribution.

Accepted Answer

The hypergeometric distribution is used when sampling without replacement from a finite population, which matches the scenario of selecting cars from a finite inventory where some have a specific defect.

Question 8

Suppose students arrive at an advising office at a rate of 30 per hour.Which of the following distributions would you use to determine the probability that the next two students will arrive 30 minutes apart?
A)Normal distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Exponential distribution.

Accepted Answer

The exponential distribution is the best choice as it models the time between arrivals in a Poisson process, where events (in this case, student arrivals) occur at a constant rate but independently of one another. In this scenario, the rate parameter (lambda) is 30 students per hour, so the time between arrivals follows an exponential distribution with lambda = 30/60 = 0.5 arrivals per minute. The probability that the next two students will arrive 30 minutes apart can then be calculated using the cumulative distribution function of the exponential distribution.

Question 9

Suppose the probability of a power outage at a nuclear power plant on a single day is the same every day of the year.Also, the probability of having a power outage on a single day does not increase or decrease the probability of a power outage on another day.Which of the following distributions would you use to determine the probability that a power outage will occur next Monday?
A)Binomial distribution.
B)Poisson distribution.
C)Normal distribution.
D)Hypergeometric distribution.

Accepted Answer

The Poisson distribution is used to model the probability of rare events occurring over a fixed time interval. In this case, the probability of a power outage at a nuclear power plant on any given day is low, and the occurrence of a power outage on one day does not affect the probability of a power outage on any other day. Therefore, the Poisson distribution is the most appropriate choice to model the probability of a power outage occurring on a single day, such as next Monday.

Question 10

Suppose the light bulbs in a factory burn out at a rate of 50 bulbs per month.Which of the following distributions would you use to determine the probability that the next two light bulbs will burn out 2 days apart?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Exponential distribution.

Accepted Answer

The Poisson distribution is the most appropriate for this scenario because it models the count of rare events over a fixed interval of time, such as the number of light bulbs burning out in a month. In addition, the question asks about the probability of two events occurring a specific time apart, which can be modeled with the exponential distribution, a continuous probability distribution commonly used to model time between rare events. Therefore, we would use the Poisson distribution to model the count of bulbs burning out, and the exponential distribution to model the time between bulb burnouts.

Question 11

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes.Which of the following distributions would you use to determine the probability that a defective light bulb will be produced in a 15 minutes interval?
A)Normal distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Exponential distribution.

Accepted Answer

The answer of Suppose the probability of producing a defective...

Question 12

The probability that a particular brand of smoke alarm will malfunction in the presence of smoke is 0.002.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at most 5,000 of them will malfunction in case of a fire?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Binomial distribution.
D)Uniform distribution.

Accepted Answer

The answer of The probability that a particular brand of...

Question 13

Suppose the probability of a car accident taking place anywhere on a stretch of a 20 miles highway is the same.Which of the following distributions would you use to determine the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?
A)Normal distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Exponential distribution.

Accepted Answer

A uniform distribution is appropriate when the probability of an event is equally likely across a continuous range. In this case, the probability of a car accident is the same across the entire 20 mile stretch of highway, making it a uniform distribution.

Question 14

Suppose the probability of finding a defective spot in an area on a piece of glass is the ratio of that area to the total area of the glass and the probability is the same across the whole glass.Which of the following distributions would you use to determine the probability of finding a defective spot in a randomly selected one square inch area on a piece of 10 feet by 10 feet glass?
A)Normal distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Exponential distribution.

Accepted Answer

The probability of finding a defective spot is proportional to the area of the spot. This is an example of a uniform distribution, where the probability is constant across the entire glass. Therefore, we can use a uniform distribution to determine the probability of finding a defective spot in any randomly selected area on the glass, including a one square inch area. A normal distribution would not be appropriate because the probabilities are not normally distributed, and neither would a Poisson distribution or an exponential distribution.

Question 15

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?
A)Uniform distribution.
B)Poisson distribution.
C)Normal distribution.
D)Exponential distribution.

Accepted Answer

The normal distribution is commonly used to model continuous variables like weights, and is a good fit when the data is approximately symmetric and bell-shaped.

Question 16

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students.Ten of the 15 students have no prior competition experience while the others have some degree of experience.Which of the following distributions would you use to determine the probability that none of the members chosen for the team have any competition experience?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Binomial distribution.

Accepted Answer

The hypergeometric distribution is appropriate here because we are selecting a specific number of individuals (4) from a larger group (15) without replacement, and we are interested in the probability of selecting a certain number of individuals with a specific characteristic (none of the members have competition experience). The Poisson distribution is not applicable because it is used to model the number of rare events in a fixed interval of time or space, and it is not clear how it would be used to model this situation. The uniform distribution is not applicable because it assumes all outcomes are equally likely, and that is not the case here. The binomial distribution is not appropriate because it assumes a fixed number of independent trials, and the number of trials here (selecting the debate team) is not fixed.

Question 17

The quality control manager of a candy plant is inspecting a batch of chocolate chip bags. When the production process is in control, the average number of blue chocolate chips per bag is 6.0.Suppose that the probability of a blue chocolate chip in a bag is constant across bags and the number of blue chocolate chips in one bag is independent of the number in any other bag.Which of the following distributions would you use to figure out the probability that any particular bag being inspected has 4.0 blue chocolate chips?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Binomial distribution.

Accepted Answer

The answer of The quality control manager of a candy...

Question 18

Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?
A)Binomial distribution.
B)Poisson distribution.
C)Normal distribution.
D)Hypergeometric distribution.

Accepted Answer

The binomial distribution is appropriate when we have a fixed number of independent, identical trials (in this case, selecting 10 students) and each trial has only two outcomes (in this case, preferring Coca-Cola or not preferring Coca-Cola). The question asks for the probability of at least half of the students preferring Coca-Cola, which is a binomial probability.

Question 19

The amount of juice that can be squeezed from a randomly selected orange out a box of oranges with approximately the same size can most likely be modeled by which of the following distributions?
A)Uniform distribution.
B)Poisson distribution.
C)Normal distribution.
D)Exponential distribution.

Accepted Answer

The normal distribution is commonly used to model continuous data, such as the amount of juice that can be squeezed from an orange, when there is no specific reason to believe that any other distribution would be accurate. The uniform distribution is appropriate when all outcomes are equally likely, but this is unlikely to be the case with the amount of juice squeezed from an orange. The Poisson distribution is typically used to model counts of rare events, while the exponential distribution is commonly used to model the time until an event occurs in a continuous process.

Question 20

It was believed that the probability of a small business that declared bankruptcy per month was the same in any month.Also, the number of small businesses that declared bankruptcy was the same every month.Which of the following distributions would you use to determine the probability that more than 3 bankruptcies will occur next month?
A)Hypergeometric distribution.
B)Poisson distribution.
C)Uniform distribution.
D)Binomial distribution.

Accepted Answer

The Poisson distribution would be the best choice in this scenario as it is used to model the probability of a certain number of events occurring in a fixed time interval, given the average rate at which they occur. Since the probability of a small business declaring bankruptcy is the same every month and the number of bankruptcies is the same every month, we can assume a constant rate of bankruptcies per month. The Poisson distribution is also appropriate for rare events, which is relevant in this scenario since we are interested in the probability of more than 3 bankruptcies (which would be considered a rare occurrence). The other distributions listed (hypergeometric, uniform, and binomial) are not appropriate in this scenario as they do not match the characteristics of the problem (such as a fixed time interval, constant rate, and rare events).

Quiz 18: A Roadmap for Analyzing Data

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women.Which of the following distributions would you use to determine the probability that half of the members will be women?

It was believed that the probability of being hit by lightning is the same during the course of a thunderstorm.Which of the following distributions would you use to determine the probability of being hit by a lightning during the first half of a thunderstorm?

Suppose students arrive at an advising office at a rate of 30 per hour.Which of the following distributions would you use to determine the probability that the next two students will arrive 30 minutes apart?

Suppose the light bulbs in a factory burn out at a rate of 50 bulbs per month.Which of the following distributions would you use to determine the probability that the next two light bulbs will burn out 2 days apart?

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes.Which of the following distributions would you use to determine the probability that a defective light bulb will be produced in a 15 minutes interval?

Suppose the probability of a car accident taking place anywhere on a stretch of a 20 miles highway is the same.Which of the following distributions would you use to determine the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

The amount of juice that can be squeezed from a randomly selected orange out a box of oranges with approximately the same size can most likely be modeled by which of the following distributions?